id	sid	tid	token	lemma	pos
ejpam-6331	1	1	european	european	PROPN
ejpam-6331	1	2	journal	journal	PROPN
ejpam-6331	1	3	of	of	ADP
ejpam-6331	1	4	pure	pure	ADJ
ejpam-6331	1	5	and	and	CCONJ
ejpam-6331	1	6	applied	applied	ADJ
ejpam-6331	1	7	mathematics	mathematic	NOUN
ejpam-6331	1	8	2025	2025	NUM
ejpam-6331	1	9	,	,	PUNCT
ejpam-6331	1	10	vol	vol	NOUN
ejpam-6331	1	11	.	.	PROPN
ejpam-6331	1	12	18	18	NUM
ejpam-6331	1	13	,	,	PUNCT
ejpam-6331	1	14	issue	issue	NOUN
ejpam-6331	1	15	3	3	NUM
ejpam-6331	1	16	,	,	PUNCT
ejpam-6331	1	17	article	article	NOUN
ejpam-6331	1	18	number	number	NOUN
ejpam-6331	1	19	6331	6331	NUM
ejpam-6331	1	20	issn	issn	PROPN
ejpam-6331	1	21	1307	1307	NUM
ejpam-6331	1	22	-	-	SYM
ejpam-6331	1	23	5543	5543	NUM
ejpam-6331	1	24	–	–	PUNCT
ejpam-6331	1	25	ejpam.com	ejpam.com	X
ejpam-6331	1	26	published	publish	VERB
ejpam-6331	1	27	by	by	ADP
ejpam-6331	1	28	new	new	PROPN
ejpam-6331	1	29	york	york	PROPN
ejpam-6331	1	30	business	business	PROPN
ejpam-6331	1	31	global	global	ADJ
ejpam-6331	1	32	complex	complex	ADJ
ejpam-6331	1	33	intuitionistic	intuitionistic	ADJ
ejpam-6331	1	34	fuzzy	fuzzy	ADJ
ejpam-6331	1	35	quasi	quasi	ADJ
ejpam-6331	1	36	-	-	ADJ
ejpam-6331	1	37	associative	associative	ADJ
ejpam-6331	1	38	ideals	ideal	NOUN
ejpam-6331	1	39	of	of	ADP
ejpam-6331	1	40	bci	bci	NOUN
ejpam-6331	1	41	-	-	PUNCT
ejpam-6331	1	42	algebras	algebras	ADJ
ejpam-6331	1	43	t.	t.	PROPN
ejpam-6331	1	44	ramesh1,2	ramesh1,2	PROPN
ejpam-6331	1	45	,	,	PUNCT
ejpam-6331	1	46	m.	m.	NOUN
ejpam-6331	1	47	balamurugan2	balamurugan2	PROPN
ejpam-6331	1	48	,	,	PUNCT
ejpam-6331	1	49	aiyared	aiyare	VERB
ejpam-6331	1	50	iampan3,∗	iampan3,∗	ADJ
ejpam-6331	1	51	1department	1department	NUM
ejpam-6331	1	52	of	of	ADP
ejpam-6331	1	53	mathematics	mathematic	NOUN
ejpam-6331	1	54	,	,	PUNCT
ejpam-6331	1	55	sri	sri	PROPN
ejpam-6331	1	56	vidya	vidya	PROPN
ejpam-6331	1	57	mandir	mandir	PROPN
ejpam-6331	1	58	arts	arts	PROPN
ejpam-6331	1	59	&	&	CCONJ
ejpam-6331	1	60	science	science	PROPN
ejpam-6331	1	61	college	college	PROPN
ejpam-6331	1	62	(	(	PUNCT
ejpam-6331	1	63	autonomous	autonomous	ADJ
ejpam-6331	1	64	)	)	PUNCT
ejpam-6331	1	65	,	,	PUNCT
ejpam-6331	1	66	uthangarai	uthangarai	X
ejpam-6331	1	67	636902	636902	NUM
ejpam-6331	1	68	,	,	PUNCT
ejpam-6331	1	69	tamil	tamil	PROPN
ejpam-6331	1	70	nadu	nadu	PROPN
ejpam-6331	1	71	,	,	PUNCT
ejpam-6331	1	72	india	india	PROPN
ejpam-6331	1	73	2department	2department	PROPN
ejpam-6331	1	74	of	of	ADP
ejpam-6331	1	75	mathematics	mathematic	NOUN
ejpam-6331	1	76	,	,	PUNCT
ejpam-6331	1	77	vel	vel	PROPN
ejpam-6331	1	78	tech	tech	PROPN
ejpam-6331	1	79	rangarajan	rangarajan	PROPN
ejpam-6331	1	80	dr	dr	PROPN
ejpam-6331	1	81	.	.	PROPN
ejpam-6331	1	82	sagunthala	sagunthala	PROPN
ejpam-6331	1	83	r&d	r&d	PROPN
ejpam-6331	1	84	institute	institute	PROPN
ejpam-6331	1	85	of	of	ADP
ejpam-6331	1	86	science	science	NOUN
ejpam-6331	1	87	and	and	CCONJ
ejpam-6331	1	88	technology	technology	NOUN
ejpam-6331	1	89	,	,	PUNCT
ejpam-6331	1	90	chennai	chennai	NOUN
ejpam-6331	1	91	600062	600062	NUM
ejpam-6331	1	92	,	,	PUNCT
ejpam-6331	1	93	tamil	tamil	PROPN
ejpam-6331	1	94	nadu	nadu	PROPN
ejpam-6331	1	95	,	,	PUNCT
ejpam-6331	1	96	india	india	PROPN
ejpam-6331	1	97	3department	3department	PROPN
ejpam-6331	1	98	of	of	ADP
ejpam-6331	1	99	mathematics	mathematic	NOUN
ejpam-6331	1	100	,	,	PUNCT
ejpam-6331	1	101	school	school	NOUN
ejpam-6331	1	102	of	of	ADP
ejpam-6331	1	103	science	science	NOUN
ejpam-6331	1	104	,	,	PUNCT
ejpam-6331	1	105	university	university	NOUN
ejpam-6331	1	106	of	of	ADP
ejpam-6331	1	107	phayao	phayao	NOUN
ejpam-6331	1	108	,	,	PUNCT
ejpam-6331	1	109	mae	mae	PROPN
ejpam-6331	1	110	ka	ka	PROPN
ejpam-6331	1	111	,	,	PUNCT
ejpam-6331	1	112	mueang	mueang	PROPN
ejpam-6331	1	113	,	,	PUNCT
ejpam-6331	1	114	phayao	phayao	NOUN
ejpam-6331	1	115	56000	56000	NUM
ejpam-6331	1	116	,	,	PUNCT
ejpam-6331	1	117	thailand	thailand	PROPN
ejpam-6331	1	118	abstract	abstract	NOUN
ejpam-6331	1	119	.	.	PUNCT
ejpam-6331	2	1	this	this	DET
ejpam-6331	2	2	paper	paper	NOUN
ejpam-6331	2	3	explores	explore	VERB
ejpam-6331	2	4	the	the	DET
ejpam-6331	2	5	application	application	NOUN
ejpam-6331	2	6	of	of	ADP
ejpam-6331	2	7	complex	complex	ADJ
ejpam-6331	2	8	intuitionistic	intuitionistic	ADJ
ejpam-6331	2	9	fuzzy	fuzzy	ADJ
ejpam-6331	2	10	sets	set	NOUN
ejpam-6331	2	11	to	to	ADP
ejpam-6331	2	12	the	the	DET
ejpam-6331	2	13	study	study	NOUN
ejpam-6331	2	14	of	of	ADP
ejpam-6331	2	15	quasi	quasi	ADJ
ejpam-6331	2	16	-	-	ADJ
ejpam-6331	2	17	associative	associative	ADJ
ejpam-6331	2	18	ideals	ideal	NOUN
ejpam-6331	2	19	in	in	ADP
ejpam-6331	2	20	bci	bci	NOUN
ejpam-6331	2	21	-	-	PUNCT
ejpam-6331	2	22	algebras	algebras	X
ejpam-6331	2	23	.	.	PUNCT
ejpam-6331	3	1	we	we	PRON
ejpam-6331	3	2	introduce	introduce	VERB
ejpam-6331	3	3	a	a	DET
ejpam-6331	3	4	new	new	ADJ
ejpam-6331	3	5	concept	concept	NOUN
ejpam-6331	3	6	—	—	PUNCT
ejpam-6331	3	7	complex	complex	ADJ
ejpam-6331	3	8	intuitionistic	intuitionistic	ADJ
ejpam-6331	3	9	fuzzy	fuzzy	ADJ
ejpam-6331	3	10	quasi	quasi	ADJ
ejpam-6331	3	11	-	-	ADJ
ejpam-6331	3	12	associative	associative	ADJ
ejpam-6331	3	13	ideals	ideal	NOUN
ejpam-6331	3	14	in	in	ADP
ejpam-6331	3	15	bci	bci	NOUN
ejpam-6331	3	16	-	-	PUNCT
ejpam-6331	3	17	algebras	algebra	NOUN
ejpam-6331	3	18	—	—	PUNCT
ejpam-6331	3	19	and	and	CCONJ
ejpam-6331	3	20	analyze	analyze	VERB
ejpam-6331	3	21	their	their	PRON
ejpam-6331	3	22	fundamental	fundamental	ADJ
ejpam-6331	3	23	properties	property	NOUN
ejpam-6331	3	24	.	.	PUNCT
ejpam-6331	4	1	the	the	DET
ejpam-6331	4	2	relationships	relationship	NOUN
ejpam-6331	4	3	between	between	ADP
ejpam-6331	4	4	complex	complex	ADJ
ejpam-6331	4	5	intuitionistic	intuitionistic	ADJ
ejpam-6331	4	6	fuzzy	fuzzy	ADJ
ejpam-6331	4	7	ideals	ideal	NOUN
ejpam-6331	4	8	and	and	CCONJ
ejpam-6331	4	9	complex	complex	ADJ
ejpam-6331	4	10	intuitionistic	intuitionistic	ADJ
ejpam-6331	4	11	fuzzy	fuzzy	ADJ
ejpam-6331	4	12	quasiassociative	quasiassociative	ADJ
ejpam-6331	4	13	ideals	ideal	NOUN
ejpam-6331	4	14	are	be	AUX
ejpam-6331	4	15	thoroughly	thoroughly	ADV
ejpam-6331	4	16	investigated	investigate	VERB
ejpam-6331	4	17	.	.	PUNCT
ejpam-6331	5	1	furthermore	furthermore	ADV
ejpam-6331	5	2	,	,	PUNCT
ejpam-6331	5	3	we	we	PRON
ejpam-6331	5	4	present	present	VERB
ejpam-6331	5	5	key	key	ADJ
ejpam-6331	5	6	characterizations	characterization	NOUN
ejpam-6331	5	7	of	of	ADP
ejpam-6331	5	8	these	these	DET
ejpam-6331	5	9	quasi	quasi	ADJ
ejpam-6331	5	10	-	-	ADJ
ejpam-6331	5	11	associative	associative	ADJ
ejpam-6331	5	12	ideals	ideal	NOUN
ejpam-6331	5	13	,	,	PUNCT
ejpam-6331	5	14	providing	provide	VERB
ejpam-6331	5	15	deeper	deep	ADJ
ejpam-6331	5	16	insights	insight	NOUN
ejpam-6331	5	17	into	into	ADP
ejpam-6331	5	18	their	their	PRON
ejpam-6331	5	19	structure	structure	NOUN
ejpam-6331	5	20	and	and	CCONJ
ejpam-6331	5	21	role	role	NOUN
ejpam-6331	5	22	within	within	ADP
ejpam-6331	5	23	bcialgebraic	bcialgebraic	ADJ
ejpam-6331	5	24	systems	system	NOUN
ejpam-6331	5	25	.	.	PUNCT
ejpam-6331	6	1	finally	finally	ADV
ejpam-6331	6	2	,	,	PUNCT
ejpam-6331	6	3	we	we	PRON
ejpam-6331	6	4	prove	prove	VERB
ejpam-6331	6	5	that	that	SCONJ
ejpam-6331	6	6	every	every	DET
ejpam-6331	6	7	complex	complex	ADJ
ejpam-6331	6	8	intuitionistic	intuitionistic	ADJ
ejpam-6331	6	9	fuzzy	fuzzy	ADJ
ejpam-6331	6	10	b	b	NOUN
ejpam-6331	6	11	-	-	PUNCT
ejpam-6331	6	12	ideal	ideal	NOUN
ejpam-6331	6	13	is	be	AUX
ejpam-6331	6	14	a	a	DET
ejpam-6331	6	15	complex	complex	ADJ
ejpam-6331	6	16	intuitionistic	intuitionistic	ADJ
ejpam-6331	6	17	fuzzy	fuzzy	ADJ
ejpam-6331	6	18	quasi	quasi	ADJ
ejpam-6331	6	19	-	-	ADJ
ejpam-6331	6	20	associative	associative	ADJ
ejpam-6331	6	21	ideal	ideal	NOUN
ejpam-6331	6	22	in	in	ADP
ejpam-6331	6	23	bci	bci	NOUN
ejpam-6331	6	24	-	-	PUNCT
ejpam-6331	6	25	algebras	algebra	NOUN
ejpam-6331	6	26	.	.	PUNCT
ejpam-6331	7	1	2020	2020	NUM
ejpam-6331	7	2	mathematics	mathematics	PROPN
ejpam-6331	7	3	subject	subject	NOUN
ejpam-6331	7	4	classifications	classification	NOUN
ejpam-6331	7	5	:	:	PUNCT
ejpam-6331	7	6	06f35	06f35	NUM
ejpam-6331	7	7	,	,	PUNCT
ejpam-6331	7	8	08a72	08a72	NUM
ejpam-6331	7	9	,	,	PUNCT
ejpam-6331	7	10	03b47	03b47	NOUN
ejpam-6331	7	11	,	,	PUNCT
ejpam-6331	7	12	30e10	30e10	NUM
ejpam-6331	7	13	key	key	ADJ
ejpam-6331	7	14	words	word	NOUN
ejpam-6331	7	15	and	and	CCONJ
ejpam-6331	7	16	phrases	phrase	NOUN
ejpam-6331	7	17	:	:	PUNCT
ejpam-6331	7	18	bci	bci	NOUN
ejpam-6331	7	19	-	-	NOUN
ejpam-6331	7	20	algebra	algebra	ADJ
ejpam-6331	7	21	,	,	PUNCT
ejpam-6331	7	22	complex	complex	ADJ
ejpam-6331	7	23	intuitionistic	intuitionistic	ADJ
ejpam-6331	7	24	fuzzy	fuzzy	ADJ
ejpam-6331	7	25	quasi	quasi	ADJ
ejpam-6331	7	26	-	-	ADJ
ejpam-6331	7	27	associative	associative	ADJ
ejpam-6331	7	28	ideal	ideal	ADJ
ejpam-6331	7	29	,	,	PUNCT
ejpam-6331	7	30	complex	complex	ADJ
ejpam-6331	7	31	intuitionistic	intuitionistic	ADJ
ejpam-6331	7	32	fuzzy	fuzzy	ADJ
ejpam-6331	7	33	b	b	NOUN
ejpam-6331	7	34	-	-	PUNCT
ejpam-6331	7	35	ideal	ideal	ADJ
ejpam-6331	7	36	1	1	NUM
ejpam-6331	7	37	.	.	PUNCT
ejpam-6331	7	38	introduction	introduction	NOUN
ejpam-6331	7	39	the	the	DET
ejpam-6331	7	40	concept	concept	NOUN
ejpam-6331	7	41	of	of	ADP
ejpam-6331	7	42	fuzzy	fuzzy	ADJ
ejpam-6331	7	43	sets	set	NOUN
ejpam-6331	7	44	(	(	PUNCT
ejpam-6331	7	45	fss	fss	NOUN
ejpam-6331	7	46	)	)	PUNCT
ejpam-6331	7	47	,	,	PUNCT
ejpam-6331	7	48	introduced	introduce	VERB
ejpam-6331	7	49	by	by	ADP
ejpam-6331	7	50	zadeh	zadeh	PROPN
ejpam-6331	7	51	in	in	ADP
ejpam-6331	7	52	1965	1965	NUM
ejpam-6331	7	53	,	,	PUNCT
ejpam-6331	7	54	revolutionized	revolutionize	VERB
ejpam-6331	7	55	the	the	DET
ejpam-6331	7	56	modeling	modeling	NOUN
ejpam-6331	7	57	of	of	ADP
ejpam-6331	7	58	uncertainty	uncertainty	NOUN
ejpam-6331	7	59	and	and	CCONJ
ejpam-6331	7	60	vagueness	vagueness	NOUN
ejpam-6331	7	61	in	in	ADP
ejpam-6331	7	62	mathematical	mathematical	ADJ
ejpam-6331	7	63	structures	structure	NOUN
ejpam-6331	7	64	[	[	X
ejpam-6331	7	65	1	1	NUM
ejpam-6331	7	66	]	]	PUNCT
ejpam-6331	7	67	.	.	PUNCT
ejpam-6331	8	1	by	by	ADP
ejpam-6331	8	2	extending	extend	VERB
ejpam-6331	8	3	classical	classical	ADJ
ejpam-6331	8	4	set	set	NOUN
ejpam-6331	8	5	theory	theory	NOUN
ejpam-6331	8	6	,	,	PUNCT
ejpam-6331	8	7	fss	fss	PROPN
ejpam-6331	8	8	enabled	enable	VERB
ejpam-6331	8	9	the	the	DET
ejpam-6331	8	10	representation	representation	NOUN
ejpam-6331	8	11	of	of	ADP
ejpam-6331	8	12	partial	partial	ADJ
ejpam-6331	8	13	membership	membership	NOUN
ejpam-6331	8	14	,	,	PUNCT
ejpam-6331	8	15	leading	lead	VERB
ejpam-6331	8	16	to	to	ADP
ejpam-6331	8	17	widespread	widespread	ADJ
ejpam-6331	8	18	applications	application	NOUN
ejpam-6331	8	19	in	in	ADP
ejpam-6331	8	20	control	control	NOUN
ejpam-6331	8	21	systems	system	NOUN
ejpam-6331	8	22	,	,	PUNCT
ejpam-6331	8	23	decision	decision	NOUN
ejpam-6331	8	24	-	-	PUNCT
ejpam-6331	8	25	making	making	NOUN
ejpam-6331	8	26	,	,	PUNCT
ejpam-6331	8	27	and	and	CCONJ
ejpam-6331	8	28	beyond	beyond	ADP
ejpam-6331	8	29	.	.	PUNCT
ejpam-6331	9	1	rosenfeld	rosenfeld	PROPN
ejpam-6331	9	2	(	(	PUNCT
ejpam-6331	9	3	1971	1971	NUM
ejpam-6331	9	4	)	)	PUNCT
ejpam-6331	9	5	advanced	advance	VERB
ejpam-6331	9	6	the	the	DET
ejpam-6331	9	7	theory	theory	NOUN
ejpam-6331	9	8	further	far	ADV
ejpam-6331	9	9	by	by	ADP
ejpam-6331	9	10	introducing	introduce	VERB
ejpam-6331	9	11	fuzzy	fuzzy	ADJ
ejpam-6331	9	12	groups	group	NOUN
ejpam-6331	9	13	,	,	PUNCT
ejpam-6331	9	14	which	which	DET
ejpam-6331	9	15	integrated	integrate	VERB
ejpam-6331	9	16	group	group	NOUN
ejpam-6331	9	17	theory	theory	NOUN
ejpam-6331	9	18	with	with	ADP
ejpam-6331	9	19	fuzzy	fuzzy	ADJ
ejpam-6331	9	20	logic	logic	NOUN
ejpam-6331	9	21	to	to	PART
ejpam-6331	9	22	study	study	VERB
ejpam-6331	9	23	algebraic	algebraic	ADJ
ejpam-6331	9	24	structures	structure	NOUN
ejpam-6331	9	25	under	under	ADP
ejpam-6331	9	26	uncertainty	uncertainty	NOUN
ejpam-6331	9	27	[	[	X
ejpam-6331	9	28	2	2	NUM
ejpam-6331	9	29	]	]	PUNCT
ejpam-6331	9	30	.	.	PUNCT
ejpam-6331	10	1	the	the	DET
ejpam-6331	10	2	foundational	foundational	ADJ
ejpam-6331	10	3	work	work	NOUN
ejpam-6331	10	4	of	of	ADP
ejpam-6331	10	5	imai	imai	PROPN
ejpam-6331	10	6	and	and	CCONJ
ejpam-6331	10	7	iséki	iséki	NUM
ejpam-6331	10	8	(	(	PUNCT
ejpam-6331	10	9	1966	1966	NUM
ejpam-6331	10	10	)	)	PUNCT
ejpam-6331	10	11	established	establish	VERB
ejpam-6331	10	12	the	the	DET
ejpam-6331	10	13	axiom	axiom	NOUN
ejpam-6331	10	14	systems	system	NOUN
ejpam-6331	10	15	for	for	ADP
ejpam-6331	10	16	bck	bck	NOUN
ejpam-6331	10	17	-	-	PUNCT
ejpam-6331	10	18	algebras	algebra	NOUN
ejpam-6331	10	19	,	,	PUNCT
ejpam-6331	10	20	bridging	bridge	VERB
ejpam-6331	10	21	logical	logical	ADJ
ejpam-6331	10	22	frameworks	framework	NOUN
ejpam-6331	10	23	with	with	ADP
ejpam-6331	10	24	algebraic	algebraic	ADJ
ejpam-6331	10	25	formalism	formalism	NOUN
ejpam-6331	10	26	[	[	X
ejpam-6331	10	27	3	3	NUM
ejpam-6331	10	28	,	,	PUNCT
ejpam-6331	10	29	4	4	NUM
ejpam-6331	10	30	]	]	PUNCT
ejpam-6331	10	31	.	.	PUNCT
ejpam-6331	10	32	iséki	iséki	PUNCT
ejpam-6331	10	33	and	and	CCONJ
ejpam-6331	10	34	∗corresponding	∗corresponde	VERB
ejpam-6331	10	35	author	author	NOUN
ejpam-6331	10	36	.	.	PUNCT
ejpam-6331	11	1	doi	doi	NOUN
ejpam-6331	11	2	:	:	PUNCT
ejpam-6331	11	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6331	https://doi.org/10.29020/nybg.ejpam.v18i3.6331	ADP
ejpam-6331	11	4	email	email	NOUN
ejpam-6331	11	5	addresses	address	VERB
ejpam-6331	11	6	:	:	PUNCT
ejpam-6331	12	1	ramesh1000.d@gmail.com	ramesh1000.d@gmail.com	PROPN
ejpam-6331	12	2	(	(	PUNCT
ejpam-6331	12	3	t.	t.	PROPN
ejpam-6331	12	4	ramesh	ramesh	PROPN
ejpam-6331	12	5	)	)	PUNCT
ejpam-6331	12	6	,	,	PUNCT
ejpam-6331	12	7	drbalamuruganm@veltech.edu.in	drbalamuruganm@veltech.edu.in	PROPN
ejpam-6331	12	8	(	(	PUNCT
ejpam-6331	12	9	m.	m.	NOUN
ejpam-6331	12	10	balamurugan	balamurugan	PROPN
ejpam-6331	12	11	)	)	PUNCT
ejpam-6331	12	12	,	,	PUNCT
ejpam-6331	12	13	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-6331	12	14	(	(	PUNCT
ejpam-6331	12	15	aiyared	aiyare	VERB
ejpam-6331	12	16	iampan	iampan	PROPN
ejpam-6331	12	17	)	)	PUNCT
ejpam-6331	12	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6331	12	19	1	1	NUM
ejpam-6331	12	20	copyright	copyright	NOUN
ejpam-6331	12	21	:	:	PUNCT
ejpam-6331	12	22	©	©	PROPN
ejpam-6331	12	23	2025	2025	NUM
ejpam-6331	12	24	the	the	DET
ejpam-6331	12	25	author(s	author(s	NOUN
ejpam-6331	12	26	)	)	PUNCT
ejpam-6331	12	27	.	.	PUNCT
ejpam-6331	13	1	(	(	PUNCT
ejpam-6331	13	2	cc	cc	NOUN
ejpam-6331	13	3	by	by	ADP
ejpam-6331	13	4	-	-	PUNCT
ejpam-6331	13	5	nc	nc	PROPN
ejpam-6331	13	6	4.0	4.0	NUM
ejpam-6331	13	7	)	)	PUNCT
ejpam-6331	13	8	t.	t.	PROPN
ejpam-6331	13	9	ramesh	ramesh	PROPN
ejpam-6331	13	10	,	,	PUNCT
ejpam-6331	13	11	m.	m.	NOUN
ejpam-6331	13	12	balamurugan	balamurugan	PROPN
ejpam-6331	13	13	,	,	PUNCT
ejpam-6331	13	14	a.	a.	NOUN
ejpam-6331	13	15	iampan	iampan	PROPN
ejpam-6331	13	16	/	/	SYM
ejpam-6331	13	17	eur	eur	PROPN
ejpam-6331	13	18	.	.	PUNCT
ejpam-6331	14	1	j.	j.	PROPN
ejpam-6331	14	2	pure	pure	PROPN
ejpam-6331	14	3	appl	appl	PROPN
ejpam-6331	14	4	.	.	PROPN
ejpam-6331	14	5	math	math	PROPN
ejpam-6331	14	6	,	,	PUNCT
ejpam-6331	14	7	18	18	NUM
ejpam-6331	14	8	(	(	PUNCT
ejpam-6331	14	9	3	3	NUM
ejpam-6331	14	10	)	)	PUNCT
ejpam-6331	14	11	(	(	PUNCT
ejpam-6331	14	12	2025	2025	NUM
ejpam-6331	14	13	)	)	PUNCT
ejpam-6331	14	14	,	,	PUNCT
ejpam-6331	14	15	6331	6331	NUM
ejpam-6331	14	16	2	2	NUM
ejpam-6331	14	17	of	of	ADP
ejpam-6331	14	18	14	14	NUM
ejpam-6331	14	19	tanaka	tanaka	NOUN
ejpam-6331	14	20	(	(	PUNCT
ejpam-6331	14	21	1978	1978	NUM
ejpam-6331	14	22	)	)	PUNCT
ejpam-6331	14	23	later	later	ADV
ejpam-6331	14	24	provided	provide	VERB
ejpam-6331	14	25	a	a	DET
ejpam-6331	14	26	comprehensive	comprehensive	ADJ
ejpam-6331	14	27	introduction	introduction	NOUN
ejpam-6331	14	28	to	to	PART
ejpam-6331	14	29	bck	bck	VERB
ejpam-6331	14	30	-	-	PUNCT
ejpam-6331	14	31	algebra	algebra	NOUN
ejpam-6331	14	32	theory	theory	NOUN
ejpam-6331	14	33	,	,	PUNCT
ejpam-6331	14	34	laying	lay	VERB
ejpam-6331	14	35	the	the	DET
ejpam-6331	14	36	groundwork	groundwork	NOUN
ejpam-6331	14	37	for	for	ADP
ejpam-6331	14	38	exploring	explore	VERB
ejpam-6331	14	39	their	their	PRON
ejpam-6331	14	40	structural	structural	ADJ
ejpam-6331	14	41	properties	property	NOUN
ejpam-6331	14	42	and	and	CCONJ
ejpam-6331	14	43	mathematical	mathematical	ADJ
ejpam-6331	14	44	applications	application	NOUN
ejpam-6331	14	45	[	[	X
ejpam-6331	14	46	5	5	NUM
ejpam-6331	14	47	]	]	PUNCT
ejpam-6331	14	48	.	.	PUNCT
ejpam-6331	15	1	zhang	zhang	X
ejpam-6331	16	1	[	[	X
ejpam-6331	16	2	6	6	NUM
ejpam-6331	16	3	]	]	PUNCT
ejpam-6331	16	4	introduced	introduce	VERB
ejpam-6331	16	5	quasi	quasi	ADJ
ejpam-6331	16	6	-	-	ADJ
ejpam-6331	16	7	associative	associative	ADJ
ejpam-6331	16	8	ideals	ideal	NOUN
ejpam-6331	16	9	in	in	ADP
ejpam-6331	16	10	bci	bci	NOUN
ejpam-6331	16	11	-	-	PUNCT
ejpam-6331	16	12	algebras	algebras	X
ejpam-6331	16	13	.	.	PUNCT
ejpam-6331	17	1	the	the	DET
ejpam-6331	17	2	integration	integration	NOUN
ejpam-6331	17	3	of	of	ADP
ejpam-6331	17	4	fuzzy	fuzzy	ADJ
ejpam-6331	17	5	logic	logic	NOUN
ejpam-6331	17	6	with	with	ADP
ejpam-6331	17	7	bck	bck	PROPN
ejpam-6331	17	8	-	-	PUNCT
ejpam-6331	17	9	algebras	algebras	PROPN
ejpam-6331	17	10	was	be	AUX
ejpam-6331	17	11	pioneered	pioneer	VERB
ejpam-6331	17	12	by	by	ADP
ejpam-6331	17	13	xi	xi	PROPN
ejpam-6331	17	14	(	(	PUNCT
ejpam-6331	17	15	1991	1991	NUM
ejpam-6331	17	16	)	)	PUNCT
ejpam-6331	17	17	,	,	PUNCT
ejpam-6331	17	18	who	who	PRON
ejpam-6331	17	19	introduced	introduce	VERB
ejpam-6331	17	20	fuzzy	fuzzy	ADJ
ejpam-6331	17	21	bck	bck	NOUN
ejpam-6331	17	22	-	-	PUNCT
ejpam-6331	17	23	algebras	algebras	PROPN
ejpam-6331	17	24	to	to	PART
ejpam-6331	17	25	study	study	VERB
ejpam-6331	17	26	algebraic	algebraic	ADJ
ejpam-6331	17	27	structures	structure	NOUN
ejpam-6331	17	28	under	under	ADP
ejpam-6331	17	29	uncertainty	uncertainty	NOUN
ejpam-6331	17	30	[	[	X
ejpam-6331	17	31	7	7	NUM
ejpam-6331	17	32	]	]	PUNCT
ejpam-6331	17	33	.	.	PUNCT
ejpam-6331	18	1	ahmad	ahmad	PROPN
ejpam-6331	18	2	(	(	PUNCT
ejpam-6331	18	3	1993	1993	NUM
ejpam-6331	18	4	)	)	PUNCT
ejpam-6331	18	5	extended	extend	VERB
ejpam-6331	18	6	this	this	DET
ejpam-6331	18	7	framework	framework	NOUN
ejpam-6331	18	8	to	to	PART
ejpam-6331	18	9	fuzzy	fuzzy	ADJ
ejpam-6331	18	10	bci	bci	NOUN
ejpam-6331	18	11	-	-	PUNCT
ejpam-6331	18	12	algebras	algebras	X
ejpam-6331	18	13	,	,	PUNCT
ejpam-6331	18	14	deepening	deepen	VERB
ejpam-6331	18	15	the	the	DET
ejpam-6331	18	16	understanding	understanding	NOUN
ejpam-6331	18	17	of	of	ADP
ejpam-6331	18	18	fuzzy	fuzzy	ADJ
ejpam-6331	18	19	algebraic	algebraic	ADJ
ejpam-6331	18	20	systems	system	NOUN
ejpam-6331	18	21	[	[	X
ejpam-6331	18	22	8	8	NUM
ejpam-6331	18	23	]	]	PUNCT
ejpam-6331	18	24	.	.	PUNCT
ejpam-6331	19	1	jun	jun	PROPN
ejpam-6331	19	2	and	and	CCONJ
ejpam-6331	19	3	song	song	NOUN
ejpam-6331	19	4	(	(	PUNCT
ejpam-6331	19	5	2012	2012	NUM
ejpam-6331	19	6	)	)	PUNCT
ejpam-6331	19	7	contributed	contribute	VERB
ejpam-6331	19	8	to	to	ADP
ejpam-6331	19	9	the	the	DET
ejpam-6331	19	10	field	field	NOUN
ejpam-6331	19	11	by	by	ADP
ejpam-6331	19	12	examining	examine	VERB
ejpam-6331	19	13	falling	fall	VERB
ejpam-6331	19	14	fuzzy	fuzzy	ADJ
ejpam-6331	19	15	quasi	quasi	ADJ
ejpam-6331	19	16	-	-	ADJ
ejpam-6331	19	17	associative	associative	ADJ
ejpam-6331	19	18	ideals	ideal	NOUN
ejpam-6331	19	19	in	in	ADP
ejpam-6331	19	20	bci	bci	NOUN
ejpam-6331	19	21	-	-	PUNCT
ejpam-6331	19	22	algebras	algebra	NOUN
ejpam-6331	19	23	,	,	PUNCT
ejpam-6331	19	24	thereby	thereby	ADV
ejpam-6331	19	25	enriching	enrich	VERB
ejpam-6331	19	26	the	the	DET
ejpam-6331	19	27	study	study	NOUN
ejpam-6331	19	28	of	of	ADP
ejpam-6331	19	29	non	non	ADJ
ejpam-6331	19	30	-	-	ADJ
ejpam-6331	19	31	associative	associative	ADJ
ejpam-6331	19	32	fuzzy	fuzzy	ADJ
ejpam-6331	19	33	structures	structure	NOUN
ejpam-6331	19	34	[	[	X
ejpam-6331	19	35	9	9	NUM
ejpam-6331	19	36	]	]	PUNCT
ejpam-6331	19	37	.	.	PUNCT
ejpam-6331	20	1	in	in	ADP
ejpam-6331	20	2	contrast	contrast	NOUN
ejpam-6331	20	3	,	,	PUNCT
ejpam-6331	20	4	lele	lele	NOUN
ejpam-6331	20	5	and	and	CCONJ
ejpam-6331	20	6	moutari	moutari	PROPN
ejpam-6331	20	7	(	(	PUNCT
ejpam-6331	20	8	2007	2007	NUM
ejpam-6331	20	9	)	)	PUNCT
ejpam-6331	20	10	explored	explore	VERB
ejpam-6331	20	11	n	n	CCONJ
ejpam-6331	20	12	-	-	ADJ
ejpam-6331	20	13	fold	fold	ADJ
ejpam-6331	20	14	quasi	quasi	ADJ
ejpam-6331	20	15	-	-	ADJ
ejpam-6331	20	16	associative	associative	ADJ
ejpam-6331	20	17	ideals	ideal	NOUN
ejpam-6331	20	18	in	in	ADP
ejpam-6331	20	19	the	the	DET
ejpam-6331	20	20	same	same	ADJ
ejpam-6331	20	21	context	context	NOUN
ejpam-6331	21	1	[	[	X
ejpam-6331	21	2	10	10	NUM
ejpam-6331	21	3	]	]	PUNCT
ejpam-6331	21	4	.	.	PUNCT
ejpam-6331	22	1	atanassov	atanassov	PROPN
ejpam-6331	22	2	(	(	PUNCT
ejpam-6331	22	3	1986	1986	NUM
ejpam-6331	22	4	)	)	PUNCT
ejpam-6331	22	5	generalized	generalize	VERB
ejpam-6331	22	6	fss	fss	ADV
ejpam-6331	22	7	by	by	ADP
ejpam-6331	22	8	introducing	introduce	VERB
ejpam-6331	22	9	intuitionistic	intuitionistic	ADJ
ejpam-6331	22	10	fuzzy	fuzzy	ADJ
ejpam-6331	22	11	sets	set	NOUN
ejpam-6331	22	12	(	(	PUNCT
ejpam-6331	22	13	ifss	ifss	NOUN
ejpam-6331	22	14	)	)	PUNCT
ejpam-6331	22	15	,	,	PUNCT
ejpam-6331	22	16	which	which	PRON
ejpam-6331	22	17	incorporate	incorporate	VERB
ejpam-6331	22	18	degrees	degree	NOUN
ejpam-6331	22	19	of	of	ADP
ejpam-6331	22	20	membership	membership	NOUN
ejpam-6331	22	21	,	,	PUNCT
ejpam-6331	22	22	non	non	ADJ
ejpam-6331	22	23	-	-	NOUN
ejpam-6331	22	24	membership	membership	NOUN
ejpam-6331	22	25	,	,	PUNCT
ejpam-6331	22	26	and	and	CCONJ
ejpam-6331	22	27	hesitation	hesitation	NOUN
ejpam-6331	22	28	to	to	PART
ejpam-6331	22	29	model	model	VERB
ejpam-6331	22	30	uncertainty	uncertainty	NOUN
ejpam-6331	22	31	more	more	ADV
ejpam-6331	22	32	robustly	robustly	ADV
ejpam-6331	22	33	[	[	X
ejpam-6331	22	34	11	11	NUM
ejpam-6331	22	35	]	]	PUNCT
ejpam-6331	22	36	.	.	PUNCT
ejpam-6331	23	1	jun	jun	PROPN
ejpam-6331	23	2	and	and	CCONJ
ejpam-6331	23	3	kim	kim	PROPN
ejpam-6331	23	4	(	(	PUNCT
ejpam-6331	23	5	2000	2000	NUM
ejpam-6331	23	6	)	)	PUNCT
ejpam-6331	23	7	applied	apply	VERB
ejpam-6331	23	8	this	this	DET
ejpam-6331	23	9	framework	framework	NOUN
ejpam-6331	23	10	to	to	PART
ejpam-6331	23	11	bck	bck	VERB
ejpam-6331	23	12	-	-	PUNCT
ejpam-6331	23	13	algebras	algebra	VERB
ejpam-6331	23	14	by	by	ADP
ejpam-6331	23	15	investigating	investigate	VERB
ejpam-6331	23	16	intuitionistic	intuitionistic	ADJ
ejpam-6331	23	17	fuzzy	fuzzy	ADJ
ejpam-6331	23	18	ideals	ideal	NOUN
ejpam-6331	23	19	(	(	PUNCT
ejpam-6331	23	20	ifids	ifid	NOUN
ejpam-6331	23	21	)	)	PUNCT
ejpam-6331	23	22	,	,	PUNCT
ejpam-6331	23	23	adding	add	VERB
ejpam-6331	23	24	a	a	DET
ejpam-6331	23	25	new	new	ADJ
ejpam-6331	23	26	dimension	dimension	NOUN
ejpam-6331	23	27	to	to	ADP
ejpam-6331	23	28	their	their	PRON
ejpam-6331	23	29	algebraic	algebraic	ADJ
ejpam-6331	23	30	structure	structure	NOUN
ejpam-6331	23	31	[	[	X
ejpam-6331	23	32	12	12	NUM
ejpam-6331	23	33	]	]	PUNCT
ejpam-6331	23	34	.	.	PUNCT
ejpam-6331	24	1	ramot	ramot	PROPN
ejpam-6331	24	2	et	et	PROPN
ejpam-6331	24	3	al	al	PROPN
ejpam-6331	24	4	.	.	PROPN
ejpam-6331	25	1	(	(	PUNCT
ejpam-6331	25	2	2002	2002	NUM
ejpam-6331	25	3	,	,	PUNCT
ejpam-6331	25	4	2003	2003	NUM
ejpam-6331	25	5	)	)	PUNCT
ejpam-6331	25	6	further	far	ADV
ejpam-6331	25	7	expanded	expand	VERB
ejpam-6331	25	8	the	the	DET
ejpam-6331	25	9	scope	scope	NOUN
ejpam-6331	25	10	of	of	ADP
ejpam-6331	25	11	fuzzy	fuzzy	ADJ
ejpam-6331	25	12	logic	logic	NOUN
ejpam-6331	25	13	by	by	ADP
ejpam-6331	25	14	proposing	propose	VERB
ejpam-6331	25	15	complex	complex	ADJ
ejpam-6331	25	16	fuzzy	fuzzy	ADJ
ejpam-6331	25	17	sets	set	NOUN
ejpam-6331	25	18	(	(	PUNCT
ejpam-6331	25	19	cfss	cfss	ADJ
ejpam-6331	25	20	)	)	PUNCT
ejpam-6331	25	21	and	and	CCONJ
ejpam-6331	25	22	complex	complex	ADJ
ejpam-6331	25	23	fuzzy	fuzzy	ADJ
ejpam-6331	25	24	logic	logic	NOUN
ejpam-6331	25	25	,	,	PUNCT
ejpam-6331	25	26	where	where	SCONJ
ejpam-6331	25	27	phase	phase	NOUN
ejpam-6331	25	28	components	component	NOUN
ejpam-6331	25	29	enable	enable	VERB
ejpam-6331	25	30	richer	rich	ADJ
ejpam-6331	25	31	representations	representation	NOUN
ejpam-6331	25	32	of	of	ADP
ejpam-6331	25	33	uncertainty	uncertainty	NOUN
ejpam-6331	25	34	[	[	X
ejpam-6331	25	35	13	13	NUM
ejpam-6331	25	36	,	,	PUNCT
ejpam-6331	25	37	14	14	NUM
ejpam-6331	25	38	]	]	PUNCT
ejpam-6331	25	39	.	.	PUNCT
ejpam-6331	26	1	alkouri	alkouri	PROPN
ejpam-6331	26	2	and	and	CCONJ
ejpam-6331	26	3	salleh	salleh	PROPN
ejpam-6331	26	4	(	(	PUNCT
ejpam-6331	26	5	2012	2012	NUM
ejpam-6331	26	6	)	)	PUNCT
ejpam-6331	26	7	introduced	introduce	VERB
ejpam-6331	26	8	complex	complex	ADJ
ejpam-6331	26	9	intuitionistic	intuitionistic	ADJ
ejpam-6331	26	10	fuzzy	fuzzy	ADJ
ejpam-6331	26	11	sets	set	NOUN
ejpam-6331	26	12	(	(	PUNCT
ejpam-6331	26	13	cif	cif	PROPN
ejpam-6331	26	14	-	-	PUNCT
ejpam-6331	26	15	sets	set	NOUN
ejpam-6331	26	16	)	)	PUNCT
ejpam-6331	26	17	,	,	PUNCT
ejpam-6331	26	18	combining	combine	VERB
ejpam-6331	26	19	the	the	DET
ejpam-6331	26	20	advantages	advantage	NOUN
ejpam-6331	26	21	of	of	ADP
ejpam-6331	26	22	ifss	ifss	NOUN
ejpam-6331	26	23	and	and	CCONJ
ejpam-6331	26	24	cfss	cfss	VERB
ejpam-6331	26	25	to	to	PART
ejpam-6331	26	26	model	model	VERB
ejpam-6331	26	27	uncertainty	uncertainty	NOUN
ejpam-6331	26	28	with	with	ADP
ejpam-6331	26	29	greater	great	ADJ
ejpam-6331	26	30	precision	precision	NOUN
ejpam-6331	26	31	[	[	X
ejpam-6331	26	32	15	15	NUM
ejpam-6331	26	33	]	]	PUNCT
ejpam-6331	26	34	.	.	PUNCT
ejpam-6331	27	1	deepika	deepika	PROPN
ejpam-6331	27	2	et	et	PROPN
ejpam-6331	27	3	al	al	PROPN
ejpam-6331	27	4	.	.	PUNCT
ejpam-6331	28	1	[	[	X
ejpam-6331	28	2	16	16	NUM
ejpam-6331	28	3	]	]	PUNCT
ejpam-6331	28	4	introduced	introduce	VERB
ejpam-6331	28	5	hybrid	hybrid	ADJ
ejpam-6331	28	6	quasi	quasi	NOUN
ejpam-6331	28	7	-	-	NOUN
ejpam-6331	28	8	ideals	ideal	NOUN
ejpam-6331	28	9	in	in	ADP
ejpam-6331	28	10	ternary	ternary	ADJ
ejpam-6331	28	11	semigroups	semigroup	NOUN
ejpam-6331	28	12	.	.	PUNCT
ejpam-6331	29	1	balamurugan	balamurugan	PROPN
ejpam-6331	29	2	et	et	PROPN
ejpam-6331	29	3	al	al	PROPN
ejpam-6331	29	4	.	.	PUNCT
ejpam-6331	30	1	[	[	X
ejpam-6331	30	2	15	15	NUM
ejpam-6331	30	3	,	,	PUNCT
ejpam-6331	30	4	17	17	NUM
ejpam-6331	30	5	]	]	PUNCT
ejpam-6331	30	6	investigated	investigate	VERB
ejpam-6331	30	7	complex	complex	ADJ
ejpam-6331	30	8	linear	linear	ADJ
ejpam-6331	30	9	diaphantine	diaphantine	NOUN
ejpam-6331	30	10	fuzzy	fuzzy	ADJ
ejpam-6331	30	11	ideals	ideal	NOUN
ejpam-6331	30	12	in	in	ADP
ejpam-6331	30	13	bck	bck	NOUN
ejpam-6331	30	14	-	-	PUNCT
ejpam-6331	30	15	algebras	algebras	PROPN
ejpam-6331	30	16	.	.	PUNCT
ejpam-6331	31	1	the	the	DET
ejpam-6331	31	2	structure	structure	NOUN
ejpam-6331	31	3	of	of	ADP
ejpam-6331	31	4	the	the	DET
ejpam-6331	31	5	paper	paper	NOUN
ejpam-6331	31	6	is	be	AUX
ejpam-6331	31	7	organized	organize	VERB
ejpam-6331	31	8	as	as	SCONJ
ejpam-6331	31	9	follows	follow	VERB
ejpam-6331	31	10	:	:	PUNCT
ejpam-6331	31	11	•	•	NUM
ejpam-6331	31	12	section	section	NOUN
ejpam-6331	31	13	2	2	NUM
ejpam-6331	31	14	reviews	review	NOUN
ejpam-6331	31	15	fundamental	fundamental	ADJ
ejpam-6331	31	16	definitions	definition	NOUN
ejpam-6331	31	17	of	of	ADP
ejpam-6331	31	18	bci	bci	NOUN
ejpam-6331	31	19	-	-	PUNCT
ejpam-6331	31	20	algebras	algebra	NOUN
ejpam-6331	31	21	and	and	CCONJ
ejpam-6331	31	22	cif	cif	PROPN
ejpam-6331	31	23	-	-	PUNCT
ejpam-6331	31	24	sets	set	NOUN
ejpam-6331	31	25	.	.	PUNCT
ejpam-6331	32	1	•	•	NUM
ejpam-6331	32	2	section	section	NOUN
ejpam-6331	32	3	3	3	NUM
ejpam-6331	32	4	introduces	introduce	NOUN
ejpam-6331	32	5	and	and	CCONJ
ejpam-6331	32	6	analyzes	analyze	VERB
ejpam-6331	32	7	complex	complex	ADJ
ejpam-6331	32	8	intuitionistic	intuitionistic	ADJ
ejpam-6331	32	9	fuzzy	fuzzy	ADJ
ejpam-6331	32	10	quasi	quasi	ADJ
ejpam-6331	32	11	-	-	ADJ
ejpam-6331	32	12	associative	associative	ADJ
ejpam-6331	32	13	ideals	ideal	NOUN
ejpam-6331	32	14	in	in	ADP
ejpam-6331	32	15	bci	bci	NOUN
ejpam-6331	32	16	-	-	PUNCT
ejpam-6331	32	17	algebras	algebras	X
ejpam-6331	32	18	.	.	PUNCT
ejpam-6331	33	1	•	•	NUM
ejpam-6331	33	2	section	section	NOUN
ejpam-6331	33	3	4	4	NUM
ejpam-6331	33	4	investigates	investigate	VERB
ejpam-6331	33	5	complex	complex	ADJ
ejpam-6331	33	6	intuitionistic	intuitionistic	ADJ
ejpam-6331	33	7	fuzzy	fuzzy	ADJ
ejpam-6331	33	8	b	b	NOUN
ejpam-6331	33	9	-	-	PUNCT
ejpam-6331	33	10	ideals	ideal	NOUN
ejpam-6331	33	11	and	and	CCONJ
ejpam-6331	33	12	their	their	PRON
ejpam-6331	33	13	related	related	ADJ
ejpam-6331	33	14	properties	property	NOUN
ejpam-6331	33	15	.	.	PUNCT
ejpam-6331	34	1	•	•	NUM
ejpam-6331	34	2	section	section	NOUN
ejpam-6331	34	3	5	5	NUM
ejpam-6331	34	4	concludes	conclude	VERB
ejpam-6331	34	5	with	with	ADP
ejpam-6331	34	6	findings	finding	NOUN
ejpam-6331	34	7	and	and	CCONJ
ejpam-6331	34	8	future	future	ADJ
ejpam-6331	34	9	perspectives	perspective	NOUN
ejpam-6331	34	10	.	.	PUNCT
ejpam-6331	35	1	2	2	X
ejpam-6331	35	2	.	.	X
ejpam-6331	35	3	preliminaries	preliminary	NOUN
ejpam-6331	35	4	to	to	PART
ejpam-6331	35	5	facilitate	facilitate	VERB
ejpam-6331	35	6	the	the	DET
ejpam-6331	35	7	understanding	understanding	NOUN
ejpam-6331	35	8	of	of	ADP
ejpam-6331	35	9	the	the	DET
ejpam-6331	35	10	main	main	ADJ
ejpam-6331	35	11	results	result	NOUN
ejpam-6331	35	12	,	,	PUNCT
ejpam-6331	35	13	this	this	DET
ejpam-6331	35	14	section	section	NOUN
ejpam-6331	35	15	briefly	briefly	ADV
ejpam-6331	35	16	recalls	recall	VERB
ejpam-6331	35	17	fundamental	fundamental	ADJ
ejpam-6331	35	18	concepts	concept	NOUN
ejpam-6331	35	19	related	relate	VERB
ejpam-6331	35	20	to	to	ADP
ejpam-6331	35	21	bci	bci	NOUN
ejpam-6331	35	22	-	-	PUNCT
ejpam-6331	35	23	algebras	algebra	NOUN
ejpam-6331	35	24	and	and	CCONJ
ejpam-6331	35	25	cif	cif	PROPN
ejpam-6331	35	26	-	-	PUNCT
ejpam-6331	35	27	sets	set	NOUN
ejpam-6331	35	28	.	.	PUNCT
ejpam-6331	36	1	we	we	PRON
ejpam-6331	36	2	begin	begin	VERB
ejpam-6331	36	3	by	by	ADP
ejpam-6331	36	4	reviewing	review	VERB
ejpam-6331	36	5	the	the	DET
ejpam-6331	36	6	axioms	axiom	NOUN
ejpam-6331	36	7	and	and	CCONJ
ejpam-6331	36	8	structural	structural	ADJ
ejpam-6331	36	9	properties	property	NOUN
ejpam-6331	36	10	of	of	ADP
ejpam-6331	36	11	bci	bci	NOUN
ejpam-6331	36	12	-	-	PUNCT
ejpam-6331	36	13	algebras	algebra	NOUN
ejpam-6331	36	14	,	,	PUNCT
ejpam-6331	36	15	followed	follow	VERB
ejpam-6331	36	16	by	by	ADP
ejpam-6331	36	17	essential	essential	ADJ
ejpam-6331	36	18	definitions	definition	NOUN
ejpam-6331	36	19	concerning	concern	VERB
ejpam-6331	36	20	cif	cif	PROPN
ejpam-6331	36	21	-	-	PUNCT
ejpam-6331	36	22	sets	set	NOUN
ejpam-6331	36	23	,	,	PUNCT
ejpam-6331	36	24	including	include	VERB
ejpam-6331	36	25	their	their	PRON
ejpam-6331	36	26	algebraic	algebraic	ADJ
ejpam-6331	36	27	behavior	behavior	NOUN
ejpam-6331	36	28	and	and	CCONJ
ejpam-6331	36	29	membership	membership	NOUN
ejpam-6331	36	30	representations	representation	NOUN
ejpam-6331	36	31	.	.	PUNCT
ejpam-6331	37	1	these	these	DET
ejpam-6331	37	2	preliminaries	preliminary	NOUN
ejpam-6331	37	3	lay	lie	VERB
ejpam-6331	37	4	the	the	DET
ejpam-6331	37	5	groundwork	groundwork	NOUN
ejpam-6331	37	6	for	for	ADP
ejpam-6331	37	7	the	the	DET
ejpam-6331	37	8	subsequent	subsequent	ADJ
ejpam-6331	37	9	development	development	NOUN
ejpam-6331	37	10	of	of	ADP
ejpam-6331	37	11	complex	complex	ADJ
ejpam-6331	37	12	intuitionistic	intuitionistic	ADJ
ejpam-6331	37	13	fuzzy	fuzzy	ADJ
ejpam-6331	37	14	quasi	quasi	ADJ
ejpam-6331	37	15	-	-	ADJ
ejpam-6331	37	16	associative	associative	ADJ
ejpam-6331	37	17	ideals	ideal	NOUN
ejpam-6331	37	18	.	.	PUNCT
ejpam-6331	38	1	definition	definition	NOUN
ejpam-6331	38	2	1	1	NUM
ejpam-6331	38	3	.	.	PUNCT
ejpam-6331	39	1	[	[	X
ejpam-6331	39	2	5	5	NUM
ejpam-6331	39	3	]	]	PUNCT
ejpam-6331	39	4	a	a	DET
ejpam-6331	39	5	bci	bci	NOUN
ejpam-6331	39	6	-	-	NOUN
ejpam-6331	39	7	algebra	algebra	NOUN
ejpam-6331	39	8	is	be	AUX
ejpam-6331	39	9	an	an	DET
ejpam-6331	39	10	algebra	algebra	NOUN
ejpam-6331	39	11	(	(	PUNCT
ejpam-6331	39	12	x	x	NOUN
ejpam-6331	39	13	;	;	PUNCT
ejpam-6331	39	14	∗	∗	NOUN
ejpam-6331	39	15	,	,	PUNCT
ejpam-6331	39	16	0	0	NUM
ejpam-6331	39	17	)	)	PUNCT
ejpam-6331	39	18	of	of	ADP
ejpam-6331	39	19	type	type	NOUN
ejpam-6331	39	20	(	(	PUNCT
ejpam-6331	39	21	2	2	NUM
ejpam-6331	39	22	,	,	PUNCT
ejpam-6331	39	23	0	0	NUM
ejpam-6331	39	24	)	)	PUNCT
ejpam-6331	39	25	that	that	PRON
ejpam-6331	39	26	obeys	obey	VERB
ejpam-6331	39	27	the	the	DET
ejpam-6331	39	28	axioms	axiom	NOUN
ejpam-6331	39	29	for	for	ADP
ejpam-6331	39	30	all	all	DET
ejpam-6331	39	31	⌜	⌜	PROPN
ejpam-6331	39	32	ϱ̃	ϱ̃	PROPN
ejpam-6331	39	33	⌝	⌝	PROPN
ejpam-6331	39	34	,	,	PUNCT
ejpam-6331	39	35	⌜	⌜	PROPN
ejpam-6331	39	36	ϑ̃	ϑ̃	PROPN
ejpam-6331	39	37	⌝	⌝	PROPN
ejpam-6331	39	38	,	,	PUNCT
ejpam-6331	39	39	⌜	⌜	PROPN
ejpam-6331	39	40	κ̃	κ̃	PROPN
ejpam-6331	39	41	⌝	⌝	PROPN
ejpam-6331	39	42	∈	∈	PROPN
ejpam-6331	39	43	x	x	SYM
ejpam-6331	39	44	,	,	PUNCT
ejpam-6331	39	45	(	(	PUNCT
ejpam-6331	39	46	bci-1	bci-1	X
ejpam-6331	39	47	)	)	PUNCT
ejpam-6331	39	48	(	(	PUNCT
ejpam-6331	39	49	(	(	PUNCT
ejpam-6331	39	50	⌜	⌜	NOUN
ejpam-6331	39	51	ϱ̃	ϱ̃	PROPN
ejpam-6331	39	52	⌝	⌝	PROPN
ejpam-6331	39	53	∗	∗	NOUN
ejpam-6331	39	54	⌜	⌜	PROPN
ejpam-6331	39	55	ϑ̃	ϑ̃	PROPN
ejpam-6331	39	56	⌝	⌝	PROPN
ejpam-6331	39	57	)	)	PUNCT
ejpam-6331	39	58	∗	∗	NOUN
ejpam-6331	39	59	(	(	PUNCT
ejpam-6331	39	60	⌜	⌜	NOUN
ejpam-6331	39	61	ϱ̃	ϱ̃	PROPN
ejpam-6331	39	62	⌝	⌝	PROPN
ejpam-6331	39	63	∗	∗	NOUN
ejpam-6331	39	64	⌜	⌜	PROPN
ejpam-6331	39	65	κ̃	κ̃	PROPN
ejpam-6331	39	66	⌝	⌝	PROPN
ejpam-6331	39	67	)	)	PUNCT
ejpam-6331	39	68	)	)	PUNCT
ejpam-6331	39	69	∗	∗	NOUN
ejpam-6331	39	70	(	(	PUNCT
ejpam-6331	39	71	⌜	⌜	PROPN
ejpam-6331	39	72	κ̃	κ̃	PROPN
ejpam-6331	39	73	⌝	⌝	PROPN
ejpam-6331	39	74	∗	∗	NOUN
ejpam-6331	39	75	⌜	⌜	PROPN
ejpam-6331	39	76	ϑ̃	ϑ̃	PROPN
ejpam-6331	39	77	⌝	⌝	PROPN
ejpam-6331	39	78	)	)	PUNCT
ejpam-6331	39	79	=	=	SYM
ejpam-6331	39	80	0	0	NUM
ejpam-6331	39	81	,	,	PUNCT
ejpam-6331	39	82	t.	t.	PROPN
ejpam-6331	39	83	ramesh	ramesh	PROPN
ejpam-6331	39	84	,	,	PUNCT
ejpam-6331	39	85	m.	m.	NOUN
ejpam-6331	39	86	balamurugan	balamurugan	PROPN
ejpam-6331	39	87	,	,	PUNCT
ejpam-6331	39	88	a.	a.	NOUN
ejpam-6331	39	89	iampan	iampan	PROPN
ejpam-6331	39	90	/	/	SYM
ejpam-6331	39	91	eur	eur	PROPN
ejpam-6331	39	92	.	.	PUNCT
ejpam-6331	40	1	j.	j.	PROPN
ejpam-6331	40	2	pure	pure	PROPN
ejpam-6331	40	3	appl	appl	PROPN
ejpam-6331	40	4	.	.	PROPN
ejpam-6331	40	5	math	math	PROPN
ejpam-6331	40	6	,	,	PUNCT
ejpam-6331	40	7	18	18	NUM
ejpam-6331	40	8	(	(	PUNCT
ejpam-6331	40	9	3	3	NUM
ejpam-6331	40	10	)	)	PUNCT
ejpam-6331	40	11	(	(	PUNCT
ejpam-6331	40	12	2025	2025	NUM
ejpam-6331	40	13	)	)	PUNCT
ejpam-6331	40	14	,	,	PUNCT
ejpam-6331	40	15	6331	6331	NUM
ejpam-6331	40	16	3	3	NUM
ejpam-6331	40	17	of	of	ADP
ejpam-6331	40	18	14	14	NUM
ejpam-6331	40	19	(	(	PUNCT
ejpam-6331	40	20	bci-2	bci-2	NUM
ejpam-6331	40	21	)	)	PUNCT
ejpam-6331	40	22	(	(	PUNCT
ejpam-6331	40	23	⌜	⌜	PUNCT
ejpam-6331	40	24	ϱ̃	ϱ̃	PROPN
ejpam-6331	40	25	⌝	⌝	PROPN
ejpam-6331	40	26	∗	∗	NOUN
ejpam-6331	40	27	(	(	PUNCT
ejpam-6331	40	28	⌜	⌜	NOUN
ejpam-6331	40	29	ϱ̃	ϱ̃	PROPN
ejpam-6331	40	30	⌝	⌝	PROPN
ejpam-6331	40	31	∗	∗	NOUN
ejpam-6331	40	32	⌜	⌜	PROPN
ejpam-6331	40	33	ϑ̃	ϑ̃	PROPN
ejpam-6331	40	34	⌝	⌝	PROPN
ejpam-6331	40	35	)	)	PUNCT
ejpam-6331	40	36	)	)	PUNCT
ejpam-6331	40	37	∗	∗	NOUN
ejpam-6331	40	38	⌜	⌜	PROPN
ejpam-6331	40	39	ϑ̃	ϑ̃	PROPN
ejpam-6331	40	40	⌝	⌝	PROPN
ejpam-6331	40	41	=	=	SYM
ejpam-6331	40	42	0	0	NUM
ejpam-6331	40	43	,	,	PUNCT
ejpam-6331	40	44	(	(	PUNCT
ejpam-6331	40	45	bci-3	bci-3	X
ejpam-6331	40	46	)	)	PUNCT
ejpam-6331	41	1	⌜	⌜	PUNCT
ejpam-6331	42	1	ϱ̃	ϱ̃	PROPN
ejpam-6331	42	2	⌝	⌝	PROPN
ejpam-6331	42	3	∗	∗	NOUN
ejpam-6331	42	4	⌜	⌜	PROPN
ejpam-6331	42	5	ϱ̃	ϱ̃	PROPN
ejpam-6331	42	6	⌝	⌝	PROPN
ejpam-6331	42	7	=	=	SYM
ejpam-6331	42	8	0	0	NUM
ejpam-6331	42	9	,	,	PUNCT
ejpam-6331	42	10	(	(	PUNCT
ejpam-6331	42	11	bci-4	bci-4	X
ejpam-6331	42	12	)	)	PUNCT
ejpam-6331	43	1	⌜	⌜	PUNCT
ejpam-6331	44	1	ϱ̃	ϱ̃	PROPN
ejpam-6331	44	2	⌝	⌝	PROPN
ejpam-6331	44	3	∗	∗	NOUN
ejpam-6331	44	4	⌜	⌜	PROPN
ejpam-6331	44	5	ϑ̃	ϑ̃	PROPN
ejpam-6331	44	6	⌝	⌝	PROPN
ejpam-6331	44	7	=	=	SYM
ejpam-6331	44	8	0	0	NUM
ejpam-6331	44	9	,	,	PUNCT
ejpam-6331	44	10	⌜	⌜	PROPN
ejpam-6331	44	11	ϑ̃	ϑ̃	PROPN
ejpam-6331	44	12	⌝	⌝	PROPN
ejpam-6331	44	13	∗	∗	NOUN
ejpam-6331	44	14	⌜	⌜	PROPN
ejpam-6331	44	15	ϱ̃	ϱ̃	PROPN
ejpam-6331	44	16	⌝	⌝	PROPN
ejpam-6331	44	17	=	=	SYM
ejpam-6331	44	18	0	0	NUM
ejpam-6331	44	19	⇒	⇒	NOUN
ejpam-6331	44	20	⌜	⌜	PROPN
ejpam-6331	44	21	ϱ̃	ϱ̃	PROPN
ejpam-6331	44	22	⌝	⌝	PROPN
ejpam-6331	44	23	=	=	SYM
ejpam-6331	44	24	⌜	⌜	PROPN
ejpam-6331	44	25	ϑ̃	ϑ̃	PROPN
ejpam-6331	44	26	⌝	⌝	PROPN
ejpam-6331	44	27	.	.	PUNCT
ejpam-6331	44	28	definition	definition	NOUN
ejpam-6331	44	29	2	2	NUM
ejpam-6331	45	1	.	.	PUNCT
ejpam-6331	46	1	[	[	X
ejpam-6331	46	2	3	3	NUM
ejpam-6331	46	3	,	,	PUNCT
ejpam-6331	46	4	4	4	NUM
ejpam-6331	46	5	]	]	PUNCT
ejpam-6331	46	6	a	a	DET
ejpam-6331	46	7	void	void	NOUN
ejpam-6331	46	8	subset	subset	NOUN
ejpam-6331	46	9	c	c	NOUN
ejpam-6331	46	10	is	be	AUX
ejpam-6331	46	11	an	an	DET
ejpam-6331	46	12	ideal	ideal	NOUN
ejpam-6331	46	13	if	if	SCONJ
ejpam-6331	46	14	the	the	DET
ejpam-6331	46	15	following	follow	VERB
ejpam-6331	46	16	hold	hold	NOUN
ejpam-6331	46	17	for	for	ADP
ejpam-6331	46	18	all	all	DET
ejpam-6331	46	19	⌜	⌜	PROPN
ejpam-6331	46	20	ϱ̃	ϱ̃	PROPN
ejpam-6331	46	21	⌝	⌝	PROPN
ejpam-6331	46	22	,	,	PUNCT
ejpam-6331	46	23	⌜	⌜	PROPN
ejpam-6331	46	24	ϑ̃	ϑ̃	PROPN
ejpam-6331	46	25	⌝	⌝	PROPN
ejpam-6331	46	26	∈	∈	PROPN
ejpam-6331	46	27	x	x	SYM
ejpam-6331	46	28	,	,	PUNCT
ejpam-6331	46	29	(	(	PUNCT
ejpam-6331	46	30	i-1	i-1	NUM
ejpam-6331	46	31	)	)	PUNCT
ejpam-6331	46	32	0	0	PUNCT
ejpam-6331	47	1	∈	∈	PROPN
ejpam-6331	47	2	c	c	NOUN
ejpam-6331	47	3	,	,	PUNCT
ejpam-6331	47	4	(	(	PUNCT
ejpam-6331	47	5	i-2	i-2	PROPN
ejpam-6331	47	6	)	)	PUNCT
ejpam-6331	47	7	⌜	⌜	PROPN
ejpam-6331	47	8	ϱ̃	ϱ̃	PROPN
ejpam-6331	47	9	⌝	⌝	PROPN
ejpam-6331	47	10	∗	∗	NOUN
ejpam-6331	47	11	⌜	⌜	PROPN
ejpam-6331	47	12	ϑ̃	ϑ̃	PROPN
ejpam-6331	47	13	⌝	⌝	PROPN
ejpam-6331	47	14	∈	∈	PROPN
ejpam-6331	47	15	c	c	PROPN
ejpam-6331	47	16	⇒	⇒	NOUN
ejpam-6331	47	17	⌜	⌜	PROPN
ejpam-6331	47	18	ϱ̃	ϱ̃	PROPN
ejpam-6331	47	19	⌝	⌝	PROPN
ejpam-6331	47	20	∈	∈	PROPN
ejpam-6331	47	21	c.	c.	NOUN
ejpam-6331	47	22	definition	definition	NOUN
ejpam-6331	47	23	3	3	NUM
ejpam-6331	47	24	.	.	PUNCT
ejpam-6331	48	1	[	[	X
ejpam-6331	48	2	6	6	NUM
ejpam-6331	48	3	]	]	PUNCT
ejpam-6331	48	4	a	a	DET
ejpam-6331	48	5	void	void	NOUN
ejpam-6331	48	6	subset	subset	NOUN
ejpam-6331	48	7	c	c	NOUN
ejpam-6331	48	8	is	be	AUX
ejpam-6331	48	9	quasi	quasi	ADJ
ejpam-6331	48	10	-	-	ADJ
ejpam-6331	48	11	associative	associative	ADJ
ejpam-6331	48	12	ideal	ideal	NOUN
ejpam-6331	48	13	if	if	SCONJ
ejpam-6331	48	14	the	the	DET
ejpam-6331	48	15	following	follow	VERB
ejpam-6331	48	16	hold	hold	NOUN
ejpam-6331	48	17	for	for	ADP
ejpam-6331	48	18	all	all	DET
ejpam-6331	48	19	⌜	⌜	PROPN
ejpam-6331	48	20	ϱ̃	ϱ̃	PROPN
ejpam-6331	48	21	⌝	⌝	PROPN
ejpam-6331	48	22	,	,	PUNCT
ejpam-6331	48	23	⌜	⌜	PROPN
ejpam-6331	48	24	ϑ̃	ϑ̃	PROPN
ejpam-6331	48	25	⌝	⌝	PROPN
ejpam-6331	48	26	∈	∈	PROPN
ejpam-6331	48	27	x	x	X
ejpam-6331	48	28	,	,	PUNCT
ejpam-6331	48	29	(	(	PUNCT
ejpam-6331	48	30	qai-1	qai-1	X
ejpam-6331	48	31	)	)	PUNCT
ejpam-6331	48	32	0	0	NUM
ejpam-6331	49	1	∈	∈	PROPN
ejpam-6331	49	2	c	c	NOUN
ejpam-6331	49	3	,	,	PUNCT
ejpam-6331	49	4	(	(	PUNCT
ejpam-6331	49	5	qai-2	qai-2	NOUN
ejpam-6331	49	6	)	)	PUNCT
ejpam-6331	49	7	⌜	⌜	PROPN
ejpam-6331	49	8	ϑ̃	ϑ̃	PROPN
ejpam-6331	49	9	⌝	⌝	PROPN
ejpam-6331	49	10	∈	∈	PROPN
ejpam-6331	49	11	c	c	NOUN
ejpam-6331	49	12	,	,	PUNCT
ejpam-6331	49	13	⌜	⌜	PROPN
ejpam-6331	49	14	ϱ̃	ϱ̃	PROPN
ejpam-6331	49	15	⌝	⌝	PROPN
ejpam-6331	49	16	∗	∗	NOUN
ejpam-6331	49	17	(	(	PUNCT
ejpam-6331	49	18	⌜	⌜	PROPN
ejpam-6331	49	19	ϑ̃	ϑ̃	PROPN
ejpam-6331	49	20	⌝	⌝	PROPN
ejpam-6331	49	21	∗	∗	NOUN
ejpam-6331	49	22	⌜	⌜	PROPN
ejpam-6331	49	23	κ̃	κ̃	PROPN
ejpam-6331	49	24	⌝	⌝	PROPN
ejpam-6331	49	25	)	)	PUNCT
ejpam-6331	49	26	∈	∈	PROPN
ejpam-6331	49	27	c	c	PROPN
ejpam-6331	49	28	⇒	⇒	NOUN
ejpam-6331	49	29	⌜	⌜	PROPN
ejpam-6331	49	30	ϱ̃	ϱ̃	PROPN
ejpam-6331	49	31	⌝	⌝	PROPN
ejpam-6331	49	32	∗	∗	NOUN
ejpam-6331	49	33	⌜	⌜	PROPN
ejpam-6331	49	34	κ̃	κ̃	PROPN
ejpam-6331	49	35	⌝	⌝	PROPN
ejpam-6331	49	36	∈	∈	PROPN
ejpam-6331	49	37	c.	c.	NOUN
ejpam-6331	49	38	definition	definition	NOUN
ejpam-6331	49	39	4	4	NUM
ejpam-6331	49	40	.	.	PUNCT
ejpam-6331	50	1	[	[	X
ejpam-6331	50	2	18	18	NUM
ejpam-6331	50	3	]	]	PUNCT
ejpam-6331	50	4	a	a	DET
ejpam-6331	50	5	cif	cif	PROPN
ejpam-6331	50	6	-	-	PUNCT
ejpam-6331	50	7	set	set	VERB
ejpam-6331	50	8	c	c	NOUN
ejpam-6331	50	9	defined	define	VERB
ejpam-6331	50	10	on	on	ADP
ejpam-6331	50	11	universal	universal	ADJ
ejpam-6331	50	12	set	set	NOUN
ejpam-6331	50	13	x	x	SYM
ejpam-6331	50	14	is	be	AUX
ejpam-6331	50	15	characterized	characterize	VERB
ejpam-6331	50	16	as	as	SCONJ
ejpam-6331	50	17	follows	follow	VERB
ejpam-6331	50	18	:	:	PUNCT
ejpam-6331	50	19	a	a	DET
ejpam-6331	50	20	=	=	X
ejpam-6331	50	21	{	{	PUNCT
ejpam-6331	50	22	(	(	PUNCT
ejpam-6331	50	23	⌜	⌜	PROPN
ejpam-6331	50	24	ϱ̃	ϱ̃	PROPN
ejpam-6331	50	25	⌝	⌝	PROPN
ejpam-6331	50	26	,	,	PUNCT
ejpam-6331	50	27	∅̃c(	∅̃c(	NOUN
ejpam-6331	50	28	⌜	⌜	NOUN
ejpam-6331	50	29	ϱ̃	ϱ̃	PROPN
ejpam-6331	50	30	⌝	⌝	PROPN
ejpam-6331	50	31	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	50	32	⌜	⌜	PROPN
ejpam-6331	50	33	ϱ̃	ϱ̃	PROPN
ejpam-6331	50	34	⌝	⌝	PROPN
ejpam-6331	50	35	)	)	PUNCT
ejpam-6331	50	36	,	,	PUNCT
ejpam-6331	50	37	φ̃c(	φ̃c(	VERB
ejpam-6331	50	38	⌜	⌜	NOUN
ejpam-6331	50	39	ϱ̃	ϱ̃	PROPN
ejpam-6331	50	40	⌝	⌝	PROPN
ejpam-6331	50	41	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	50	42	⌜	⌜	PROPN
ejpam-6331	50	43	ϱ̃	ϱ̃	PROPN
ejpam-6331	50	44	⌝	⌝	PROPN
ejpam-6331	50	45	)	)	PUNCT
ejpam-6331	50	46	)	)	PUNCT
ejpam-6331	50	47	,	,	PUNCT
ejpam-6331	50	48	∀	∀	PUNCT
ejpam-6331	50	49	⌜	⌜	NOUN
ejpam-6331	50	50	ϱ̃	ϱ̃	PROPN
ejpam-6331	50	51	⌝	⌝	PROPN
ejpam-6331	50	52	∈	∈	PROPN
ejpam-6331	50	53	x	x	X
ejpam-6331	50	54	}	}	PUNCT
ejpam-6331	50	55	,	,	PUNCT
ejpam-6331	50	56	where	where	SCONJ
ejpam-6331	50	57	∅̃c(	∅̃c(	NOUN
ejpam-6331	50	58	⌜	⌜	NOUN
ejpam-6331	50	59	ϱ̃	ϱ̃	PROPN
ejpam-6331	50	60	⌝	⌝	PROPN
ejpam-6331	50	61	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	50	62	⌜	⌜	PROPN
ejpam-6331	50	63	ϱ̃	ϱ̃	PROPN
ejpam-6331	50	64	⌝	⌝	PROPN
ejpam-6331	50	65	)	)	PUNCT
ejpam-6331	50	66	is	be	AUX
ejpam-6331	50	67	truth	truth	NOUN
ejpam-6331	50	68	function	function	NOUN
ejpam-6331	50	69	,	,	PUNCT
ejpam-6331	50	70	∅̃c(	∅̃c(	NOUN
ejpam-6331	50	71	⌜	⌜	NOUN
ejpam-6331	50	72	ϱ̃	ϱ̃	PROPN
ejpam-6331	50	73	⌝	⌝	PROPN
ejpam-6331	50	74	)	)	PUNCT
ejpam-6331	50	75	:	:	PUNCT
ejpam-6331	51	1	x	x	X
ejpam-6331	51	2	→	→	PUNCT
ejpam-6331	52	1	[	[	X
ejpam-6331	52	2	0	0	NUM
ejpam-6331	52	3	,	,	PUNCT
ejpam-6331	52	4	1	1	NUM
ejpam-6331	52	5	]	]	PUNCT
ejpam-6331	52	6	and	and	CCONJ
ejpam-6331	52	7	ω̃c(	ω̃c(	VERB
ejpam-6331	52	8	⌜	⌜	NOUN
ejpam-6331	52	9	ϱ̃	ϱ̃	PROPN
ejpam-6331	52	10	⌝	⌝	PROPN
ejpam-6331	52	11	)	)	PUNCT
ejpam-6331	52	12	∈	∈	PROPN
ejpam-6331	53	1	[	[	X
ejpam-6331	53	2	0	0	NUM
ejpam-6331	53	3	,	,	PUNCT
ejpam-6331	53	4	2π	2π	NOUN
ejpam-6331	53	5	]	]	PUNCT
ejpam-6331	53	6	is	be	AUX
ejpam-6331	53	7	a	a	DET
ejpam-6331	53	8	periodic	periodic	ADJ
ejpam-6331	53	9	function	function	NOUN
ejpam-6331	53	10	,	,	PUNCT
ejpam-6331	53	11	φ̃c(	φ̃c(	VERB
ejpam-6331	53	12	⌜	⌜	NOUN
ejpam-6331	53	13	ϱ̃	ϱ̃	PROPN
ejpam-6331	53	14	⌝	⌝	PROPN
ejpam-6331	53	15	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	53	16	⌜	⌜	PROPN
ejpam-6331	53	17	ϱ̃	ϱ̃	PROPN
ejpam-6331	53	18	⌝	⌝	PROPN
ejpam-6331	53	19	)	)	PUNCT
ejpam-6331	53	20	is	be	AUX
ejpam-6331	53	21	falsity	falsity	NOUN
ejpam-6331	53	22	function	function	NOUN
ejpam-6331	53	23	,	,	PUNCT
ejpam-6331	53	24	φ̃c(	φ̃c(	NOUN
ejpam-6331	53	25	⌜	⌜	NOUN
ejpam-6331	53	26	ϱ̃	ϱ̃	PROPN
ejpam-6331	53	27	⌝	⌝	PROPN
ejpam-6331	53	28	)	)	PUNCT
ejpam-6331	53	29	:	:	PUNCT
ejpam-6331	54	1	x	x	X
ejpam-6331	54	2	→	→	PUNCT
ejpam-6331	55	1	[	[	X
ejpam-6331	55	2	0	0	NUM
ejpam-6331	55	3	,	,	PUNCT
ejpam-6331	55	4	1	1	NUM
ejpam-6331	55	5	]	]	PUNCT
ejpam-6331	55	6	and	and	CCONJ
ejpam-6331	55	7	θ̃c(	θ̃c(	PROPN
ejpam-6331	55	8	⌜	⌜	PROPN
ejpam-6331	55	9	ϱ̃	ϱ̃	PROPN
ejpam-6331	55	10	⌝	⌝	PROPN
ejpam-6331	55	11	)	)	PUNCT
ejpam-6331	55	12	∈	∈	PROPN
ejpam-6331	56	1	[	[	X
ejpam-6331	56	2	0	0	NUM
ejpam-6331	56	3	,	,	PUNCT
ejpam-6331	56	4	2π	2π	NOUN
ejpam-6331	56	5	]	]	PUNCT
ejpam-6331	56	6	is	be	AUX
ejpam-6331	56	7	a	a	DET
ejpam-6331	56	8	periodic	periodic	ADJ
ejpam-6331	56	9	function	function	NOUN
ejpam-6331	56	10	.	.	PUNCT
ejpam-6331	57	1	finally	finally	ADV
ejpam-6331	57	2	0	0	NUM
ejpam-6331	57	3	≤	≤	NUM
ejpam-6331	57	4	∅̃c(	∅̃c(	NOUN
ejpam-6331	57	5	⌜	⌜	NOUN
ejpam-6331	57	6	ϱ̃	ϱ̃	PROPN
ejpam-6331	57	7	⌝	⌝	PROPN
ejpam-6331	57	8	)	)	PUNCT
ejpam-6331	58	1	+	+	SYM
ejpam-6331	58	2	φ̃c(	φ̃c(	PROPN
ejpam-6331	58	3	⌜	⌜	NOUN
ejpam-6331	58	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	58	5	⌝	⌝	PROPN
ejpam-6331	58	6	)	)	PUNCT
ejpam-6331	58	7	≤	≤	NOUN
ejpam-6331	58	8	1	1	NUM
ejpam-6331	58	9	for	for	ADP
ejpam-6331	58	10	all	all	DET
ejpam-6331	58	11	⌜	⌜	NOUN
ejpam-6331	58	12	ϱ̃	ϱ̃	PROPN
ejpam-6331	58	13	⌝	⌝	PROPN
ejpam-6331	58	14	∈	∈	PROPN
ejpam-6331	58	15	x	x	X
ejpam-6331	58	16	.	.	PUNCT
ejpam-6331	58	17	example	example	NOUN
ejpam-6331	59	1	1	1	NUM
ejpam-6331	59	2	.	.	PUNCT
ejpam-6331	59	3	let	let	VERB
ejpam-6331	59	4	x	x	PUNCT
ejpam-6331	59	5	=	=	PRON
ejpam-6331	59	6	{	{	PUNCT
ejpam-6331	59	7	⌜	⌜	PROPN
ejpam-6331	59	8	ϱ̃	ϱ̃	PROPN
ejpam-6331	59	9	⌝	⌝	PROPN
ejpam-6331	59	10	,	,	PUNCT
ejpam-6331	59	11	⌜	⌜	PROPN
ejpam-6331	59	12	ϑ̃	ϑ̃	PROPN
ejpam-6331	59	13	⌝	⌝	PROPN
ejpam-6331	59	14	,	,	PUNCT
ejpam-6331	59	15	⌜	⌜	PROPN
ejpam-6331	59	16	κ̃	κ̃	PROPN
ejpam-6331	59	17	⌝	⌝	PROPN
ejpam-6331	59	18	}	}	PUNCT
ejpam-6331	59	19	.	.	PUNCT
ejpam-6331	60	1	then	then	ADV
ejpam-6331	60	2	,	,	PUNCT
ejpam-6331	60	3	cif	cif	PROPN
ejpam-6331	60	4	-	-	PUNCT
ejpam-6331	60	5	set	set	VERB
ejpam-6331	60	6	c	c	NOUN
ejpam-6331	60	7	=	=	SYM
ejpam-6331	60	8	{	{	PUNCT
ejpam-6331	60	9	(	(	PUNCT
ejpam-6331	60	10	⌜	⌜	PROPN
ejpam-6331	60	11	ϱ̃	ϱ̃	PROPN
ejpam-6331	60	12	⌝	⌝	PROPN
ejpam-6331	60	13	,	,	PUNCT
ejpam-6331	60	14	0.7e	0.7e	VERB
ejpam-6331	60	15	iπ	iπ	ADV
ejpam-6331	60	16	6	6	NUM
ejpam-6331	60	17	,	,	PUNCT
ejpam-6331	60	18	0.2e	0.2e	VERB
ejpam-6331	60	19	iπ	iπ	ADV
ejpam-6331	60	20	4	4	NUM
ejpam-6331	60	21	)	)	PUNCT
ejpam-6331	60	22	,	,	PUNCT
ejpam-6331	60	23	(	(	PUNCT
ejpam-6331	60	24	⌜	⌜	PROPN
ejpam-6331	60	25	ϑ̃	ϑ̃	PROPN
ejpam-6331	60	26	⌝	⌝	PROPN
ejpam-6331	60	27	,	,	PUNCT
ejpam-6331	60	28	0.6e	0.6e	NOUN
ejpam-6331	60	29	iπ	iπ	DET
ejpam-6331	60	30	3	3	NUM
ejpam-6331	60	31	,	,	PUNCT
ejpam-6331	60	32	0.3e	0.3e	VERB
ejpam-6331	60	33	iπ	iπ	ADV
ejpam-6331	60	34	2	2	NUM
ejpam-6331	60	35	)	)	PUNCT
ejpam-6331	60	36	,	,	PUNCT
ejpam-6331	60	37	(	(	PUNCT
ejpam-6331	60	38	⌜	⌜	PROPN
ejpam-6331	60	39	κ̃	κ̃	PROPN
ejpam-6331	60	40	⌝	⌝	PROPN
ejpam-6331	60	41	,	,	PUNCT
ejpam-6331	60	42	0.5e	0.5e	NUM
ejpam-6331	61	1	i2π	i2π	PROPN
ejpam-6331	61	2	3	3	NUM
ejpam-6331	61	3	,	,	PUNCT
ejpam-6331	61	4	0.4e	0.4e	PROPN
ejpam-6331	61	5	i4π	i4π	PROPN
ejpam-6331	61	6	5	5	NUM
ejpam-6331	61	7	)	)	PUNCT
ejpam-6331	61	8	}	}	PUNCT
ejpam-6331	61	9	.	.	PUNCT
ejpam-6331	62	1	90	90	NUM
ejpam-6331	62	2	◦	◦	NOUN
ejpam-6331	62	3	270	270	NUM
ejpam-6331	62	4	◦	◦	NOUN
ejpam-6331	62	5	0	0	NUM
ejpam-6331	62	6	◦	◦	NOUN
ejpam-6331	62	7	180	180	NUM
ejpam-6331	62	8	◦	◦	NOUN
ejpam-6331	62	9	135	135	NUM
ejpam-6331	62	10	◦	◦	NOUN
ejpam-6331	62	11	45	45	NUM
ejpam-6331	62	12	◦	◦	NOUN
ejpam-6331	62	13	315	315	NUM
ejpam-6331	62	14	◦	◦	NOUN
ejpam-6331	62	15	225	225	NUM
ejpam-6331	62	16	◦	◦	NOUN
ejpam-6331	62	17	0.2	0.2	NUM
ejpam-6331	62	18	0.4	0.4	NUM
ejpam-6331	62	19	0.6	0.6	NUM
ejpam-6331	62	20	0.8	0.8	NUM
ejpam-6331	62	21	−	−	NUM
ejpam-6331	62	22	⌜	⌜	PUNCT
ejpam-6331	62	23	ϱ̃	ϱ̃	PROPN
ejpam-6331	62	24	⌝	⌝	PROPN
ejpam-6331	62	25	∅̃c	∅̃c	NOUN
ejpam-6331	62	26	−	−	PROPN
ejpam-6331	62	27	⌜	⌜	PROPN
ejpam-6331	62	28	ϱ̃	ϱ̃	PROPN
ejpam-6331	62	29	⌝	⌝	PROPN
ejpam-6331	62	30	φ̃c	φ̃c	NOUN
ejpam-6331	62	31	−	−	PROPN
ejpam-6331	62	32	⌜	⌜	SYM
ejpam-6331	62	33	ϑ̃	ϑ̃	PROPN
ejpam-6331	62	34	⌝	⌝	PROPN
ejpam-6331	62	35	∅̃c	∅̃c	NOUN
ejpam-6331	62	36	−	−	PROPN
ejpam-6331	62	37	⌜	⌜	PROPN
ejpam-6331	62	38	ϑ̃	ϑ̃	PROPN
ejpam-6331	62	39	⌝	⌝	PROPN
ejpam-6331	62	40	φ̃c	φ̃c	PROPN
ejpam-6331	63	1	−	−	PROPN
ejpam-6331	63	2	⌜	⌜	PROPN
ejpam-6331	63	3	κ̃	κ̃	PROPN
ejpam-6331	63	4	⌝	⌝	PROPN
ejpam-6331	63	5	∅̃c	∅̃c	NOUN
ejpam-6331	63	6	−	−	NOUN
ejpam-6331	63	7	⌜	⌜	PROPN
ejpam-6331	63	8	κ̃	κ̃	PROPN
ejpam-6331	63	9	⌝	⌝	PROPN
ejpam-6331	63	10	φ̃c	φ̃c	ADJ
ejpam-6331	63	11	3	3	NUM
ejpam-6331	63	12	.	.	PUNCT
ejpam-6331	63	13	complex	complex	ADJ
ejpam-6331	63	14	intuitionistic	intuitionistic	ADJ
ejpam-6331	63	15	fuzzy	fuzzy	ADJ
ejpam-6331	63	16	quasi	quasi	ADJ
ejpam-6331	63	17	-	-	ADJ
ejpam-6331	63	18	associative	associative	ADJ
ejpam-6331	63	19	ideals	ideal	NOUN
ejpam-6331	63	20	in	in	ADP
ejpam-6331	63	21	this	this	DET
ejpam-6331	63	22	section	section	NOUN
ejpam-6331	63	23	,	,	PUNCT
ejpam-6331	63	24	we	we	PRON
ejpam-6331	63	25	introduce	introduce	VERB
ejpam-6331	63	26	the	the	DET
ejpam-6331	63	27	concept	concept	NOUN
ejpam-6331	63	28	of	of	ADP
ejpam-6331	63	29	complex	complex	ADJ
ejpam-6331	63	30	intuitionistic	intuitionistic	ADJ
ejpam-6331	63	31	fuzzy	fuzzy	ADJ
ejpam-6331	63	32	quasi	quasi	ADJ
ejpam-6331	63	33	-	-	ADJ
ejpam-6331	63	34	associative	associative	ADJ
ejpam-6331	63	35	ideals	ideal	NOUN
ejpam-6331	63	36	(	(	PUNCT
ejpam-6331	63	37	cifqa	cifqa	NOUN
ejpam-6331	63	38	-	-	PUNCT
ejpam-6331	63	39	ideals	ideal	NOUN
ejpam-6331	63	40	)	)	PUNCT
ejpam-6331	63	41	within	within	ADP
ejpam-6331	63	42	the	the	DET
ejpam-6331	63	43	framework	framework	NOUN
ejpam-6331	63	44	of	of	ADP
ejpam-6331	63	45	bci	bci	PROPN
ejpam-6331	63	46	-	-	PUNCT
ejpam-6331	63	47	algebras	algebra	NOUN
ejpam-6331	63	48	.	.	PUNCT
ejpam-6331	64	1	by	by	ADP
ejpam-6331	64	2	extending	extend	VERB
ejpam-6331	64	3	the	the	DET
ejpam-6331	64	4	classical	classical	ADJ
ejpam-6331	64	5	notion	notion	NOUN
ejpam-6331	64	6	of	of	ADP
ejpam-6331	64	7	quasi	quasi	ADJ
ejpam-6331	64	8	-	-	ADJ
ejpam-6331	64	9	associative	associative	ADJ
ejpam-6331	64	10	ideals	ideal	NOUN
ejpam-6331	64	11	through	through	ADP
ejpam-6331	64	12	the	the	DET
ejpam-6331	64	13	lens	lens	NOUN
ejpam-6331	64	14	of	of	ADP
ejpam-6331	64	15	complex	complex	ADJ
ejpam-6331	64	16	intuitionistic	intuitionistic	ADJ
ejpam-6331	64	17	fuzzy	fuzzy	ADJ
ejpam-6331	64	18	logic	logic	NOUN
ejpam-6331	64	19	,	,	PUNCT
ejpam-6331	64	20	we	we	PRON
ejpam-6331	64	21	t.	t.	PROPN
ejpam-6331	64	22	ramesh	ramesh	PROPN
ejpam-6331	64	23	,	,	PUNCT
ejpam-6331	64	24	m.	m.	NOUN
ejpam-6331	64	25	balamurugan	balamurugan	PROPN
ejpam-6331	64	26	,	,	PUNCT
ejpam-6331	64	27	a.	a.	NOUN
ejpam-6331	64	28	iampan	iampan	PROPN
ejpam-6331	64	29	/	/	SYM
ejpam-6331	64	30	eur	eur	PROPN
ejpam-6331	64	31	.	.	PUNCT
ejpam-6331	65	1	j.	j.	PROPN
ejpam-6331	65	2	pure	pure	PROPN
ejpam-6331	65	3	appl	appl	PROPN
ejpam-6331	65	4	.	.	PROPN
ejpam-6331	65	5	math	math	PROPN
ejpam-6331	65	6	,	,	PUNCT
ejpam-6331	65	7	18	18	NUM
ejpam-6331	65	8	(	(	PUNCT
ejpam-6331	65	9	3	3	NUM
ejpam-6331	65	10	)	)	PUNCT
ejpam-6331	65	11	(	(	PUNCT
ejpam-6331	65	12	2025	2025	NUM
ejpam-6331	65	13	)	)	PUNCT
ejpam-6331	65	14	,	,	PUNCT
ejpam-6331	65	15	6331	6331	NUM
ejpam-6331	65	16	4	4	NUM
ejpam-6331	65	17	of	of	ADP
ejpam-6331	65	18	14	14	NUM
ejpam-6331	65	19	establish	establish	VERB
ejpam-6331	65	20	new	new	ADJ
ejpam-6331	65	21	algebraic	algebraic	ADJ
ejpam-6331	65	22	structures	structure	NOUN
ejpam-6331	65	23	equipped	equip	VERB
ejpam-6331	65	24	to	to	PART
ejpam-6331	65	25	handle	handle	VERB
ejpam-6331	65	26	both	both	DET
ejpam-6331	65	27	magnitude	magnitude	NOUN
ejpam-6331	65	28	and	and	CCONJ
ejpam-6331	65	29	phase	phase	NOUN
ejpam-6331	65	30	uncertainty	uncertainty	NOUN
ejpam-6331	65	31	.	.	PUNCT
ejpam-6331	66	1	we	we	PRON
ejpam-6331	66	2	define	define	VERB
ejpam-6331	66	3	these	these	DET
ejpam-6331	66	4	ideals	ideal	NOUN
ejpam-6331	66	5	formally	formally	ADV
ejpam-6331	66	6	and	and	CCONJ
ejpam-6331	66	7	explore	explore	VERB
ejpam-6331	66	8	their	their	PRON
ejpam-6331	66	9	basic	basic	ADJ
ejpam-6331	66	10	properties	property	NOUN
ejpam-6331	66	11	and	and	CCONJ
ejpam-6331	66	12	examples	example	NOUN
ejpam-6331	66	13	to	to	PART
ejpam-6331	66	14	illustrate	illustrate	VERB
ejpam-6331	66	15	their	their	PRON
ejpam-6331	66	16	significance	significance	NOUN
ejpam-6331	66	17	and	and	CCONJ
ejpam-6331	66	18	distinct	distinct	ADJ
ejpam-6331	66	19	behavior	behavior	NOUN
ejpam-6331	66	20	.	.	PUNCT
ejpam-6331	67	1	definition	definition	NOUN
ejpam-6331	67	2	5	5	NUM
ejpam-6331	67	3	.	.	PUNCT
ejpam-6331	68	1	a	a	DET
ejpam-6331	68	2	cif	cif	PROPN
ejpam-6331	68	3	-	-	PUNCT
ejpam-6331	68	4	set	set	VERB
ejpam-6331	68	5	c	c	NOUN
ejpam-6331	68	6	=	=	SYM
ejpam-6331	68	7	(	(	PUNCT
ejpam-6331	68	8	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	68	9	,	,	PUNCT
ejpam-6331	68	10	φ̃ce	φ̃ce	PROPN
ejpam-6331	68	11	iθ̃c	iθ̃c	PROPN
ejpam-6331	68	12	)	)	PUNCT
ejpam-6331	68	13	forms	form	VERB
ejpam-6331	68	14	a	a	DET
ejpam-6331	68	15	complex	complex	ADJ
ejpam-6331	68	16	intuitionistic	intuitionistic	ADJ
ejpam-6331	68	17	fuzzy	fuzzy	ADJ
ejpam-6331	68	18	subalgebra	subalgebra	NOUN
ejpam-6331	68	19	(	(	PUNCT
ejpam-6331	68	20	cif	cif	PROPN
ejpam-6331	68	21	-	-	PUNCT
ejpam-6331	68	22	subalgebra	subalgebra	PROPN
ejpam-6331	68	23	)	)	PUNCT
ejpam-6331	68	24	if	if	SCONJ
ejpam-6331	68	25	it	it	PRON
ejpam-6331	68	26	satisfies	satisfy	VERB
ejpam-6331	68	27	the	the	DET
ejpam-6331	68	28	following	following	NOUN
ejpam-6331	68	29	:	:	PUNCT
ejpam-6331	68	30	(	(	PUNCT
ejpam-6331	68	31	cifs-1	cifs-1	NOUN
ejpam-6331	68	32	)	)	PUNCT
ejpam-6331	68	33	∅̃c(	∅̃c(	NOUN
ejpam-6331	68	34	⌜	⌜	PROPN
ejpam-6331	68	35	ϱ̃	ϱ̃	PROPN
ejpam-6331	68	36	⌝	⌝	PROPN
ejpam-6331	68	37	∗	∗	NOUN
ejpam-6331	68	38	⌜	⌜	PROPN
ejpam-6331	68	39	ϑ̃	ϑ̃	PROPN
ejpam-6331	68	40	⌝	⌝	PROPN
ejpam-6331	68	41	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	68	42	⌜	⌜	PROPN
ejpam-6331	68	43	ϱ̃	ϱ̃	PROPN
ejpam-6331	68	44	⌝	⌝	PROPN
ejpam-6331	68	45	∗	∗	NOUN
ejpam-6331	68	46	⌜	⌜	PROPN
ejpam-6331	68	47	ϑ̃	ϑ̃	PROPN
ejpam-6331	68	48	⌝	⌝	PROPN
ejpam-6331	68	49	)	)	PUNCT
ejpam-6331	68	50	≥	≥	NOUN
ejpam-6331	68	51	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	68	52	⌜	⌜	PROPN
ejpam-6331	68	53	ϱ̃	ϱ̃	PROPN
ejpam-6331	68	54	⌝	⌝	PROPN
ejpam-6331	68	55	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	68	56	⌜	⌜	PROPN
ejpam-6331	68	57	ϱ̃	ϱ̃	PROPN
ejpam-6331	68	58	⌝	⌝	PROPN
ejpam-6331	68	59	)	)	PUNCT
ejpam-6331	68	60	,	,	PUNCT
ejpam-6331	69	1	∅̃c(	∅̃c(	NOUN
ejpam-6331	69	2	⌜	⌜	SYM
ejpam-6331	69	3	ϑ̃	ϑ̃	PROPN
ejpam-6331	69	4	⌝	⌝	PROPN
ejpam-6331	69	5	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	69	6	⌜	⌜	PROPN
ejpam-6331	69	7	ϑ̃	ϑ̃	PROPN
ejpam-6331	69	8	⌝	⌝	PROPN
ejpam-6331	69	9	)	)	PUNCT
ejpam-6331	69	10	}	}	PUNCT
ejpam-6331	69	11	,	,	PUNCT
ejpam-6331	69	12	(	(	PUNCT
ejpam-6331	69	13	cifs-2	cifs-2	X
ejpam-6331	69	14	)	)	PUNCT
ejpam-6331	69	15	φ̃c(	φ̃c(	VERB
ejpam-6331	69	16	⌜	⌜	NOUN
ejpam-6331	69	17	ϱ̃	ϱ̃	PROPN
ejpam-6331	69	18	⌝	⌝	PROPN
ejpam-6331	69	19	∗	∗	NOUN
ejpam-6331	69	20	⌜	⌜	PROPN
ejpam-6331	69	21	ϑ̃	ϑ̃	PROPN
ejpam-6331	69	22	⌝	⌝	PROPN
ejpam-6331	69	23	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	69	24	⌜	⌜	PROPN
ejpam-6331	69	25	ϱ̃	ϱ̃	PROPN
ejpam-6331	69	26	⌝	⌝	PROPN
ejpam-6331	69	27	∗	∗	NOUN
ejpam-6331	69	28	⌜	⌜	PROPN
ejpam-6331	69	29	ϑ̃	ϑ̃	PROPN
ejpam-6331	69	30	⌝	⌝	PROPN
ejpam-6331	69	31	)	)	PUNCT
ejpam-6331	69	32	≤	≤	NOUN
ejpam-6331	69	33	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	69	34	⌜	⌜	PROPN
ejpam-6331	69	35	ϱ̃	ϱ̃	PROPN
ejpam-6331	69	36	⌝	⌝	PROPN
ejpam-6331	69	37	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	69	38	⌜	⌜	PROPN
ejpam-6331	69	39	ϱ̃	ϱ̃	PROPN
ejpam-6331	69	40	⌝	⌝	PROPN
ejpam-6331	69	41	)	)	PUNCT
ejpam-6331	69	42	,	,	PUNCT
ejpam-6331	69	43	φ̃c(	φ̃c(	PROPN
ejpam-6331	69	44	⌜	⌜	PROPN
ejpam-6331	69	45	ϑ̃	ϑ̃	PROPN
ejpam-6331	69	46	⌝	⌝	PROPN
ejpam-6331	69	47	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	69	48	⌜	⌜	PROPN
ejpam-6331	69	49	ϑ̃	ϑ̃	PROPN
ejpam-6331	69	50	⌝	⌝	PROPN
ejpam-6331	69	51	)	)	PUNCT
ejpam-6331	69	52	}	}	PUNCT
ejpam-6331	69	53	,	,	PUNCT
ejpam-6331	69	54	for	for	ADP
ejpam-6331	69	55	all	all	DET
ejpam-6331	69	56	⌜	⌜	PROPN
ejpam-6331	69	57	ϱ̃	ϱ̃	PROPN
ejpam-6331	69	58	⌝	⌝	PROPN
ejpam-6331	69	59	,	,	PUNCT
ejpam-6331	69	60	⌜	⌜	PROPN
ejpam-6331	69	61	ϑ̃	ϑ̃	PROPN
ejpam-6331	69	62	⌝	⌝	PROPN
ejpam-6331	69	63	∈	∈	PROPN
ejpam-6331	69	64	x	x	X
ejpam-6331	69	65	.	.	PUNCT
ejpam-6331	70	1	definition	definition	NOUN
ejpam-6331	70	2	6	6	NUM
ejpam-6331	70	3	.	.	PUNCT
ejpam-6331	71	1	a	a	DET
ejpam-6331	71	2	cif	cif	PROPN
ejpam-6331	71	3	-	-	PUNCT
ejpam-6331	71	4	set	set	VERB
ejpam-6331	71	5	c	c	NOUN
ejpam-6331	71	6	=	=	SYM
ejpam-6331	71	7	(	(	PUNCT
ejpam-6331	71	8	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	71	9	,	,	PUNCT
ejpam-6331	71	10	φ̃ce	φ̃ce	PROPN
ejpam-6331	71	11	iθ̃c	iθ̃c	PROPN
ejpam-6331	71	12	)	)	PUNCT
ejpam-6331	71	13	forms	form	VERB
ejpam-6331	71	14	a	a	DET
ejpam-6331	71	15	complex	complex	ADJ
ejpam-6331	71	16	intuitionistic	intuitionistic	ADJ
ejpam-6331	71	17	fuzzy	fuzzy	ADJ
ejpam-6331	71	18	ideal	ideal	NOUN
ejpam-6331	71	19	(	(	PUNCT
ejpam-6331	71	20	cif	cif	PROPN
ejpam-6331	71	21	-	-	PUNCT
ejpam-6331	71	22	ideal	ideal	NOUN
ejpam-6331	71	23	)	)	PUNCT
ejpam-6331	71	24	if	if	SCONJ
ejpam-6331	71	25	it	it	PRON
ejpam-6331	71	26	satisfies	satisfy	VERB
ejpam-6331	71	27	the	the	DET
ejpam-6331	71	28	following	following	NOUN
ejpam-6331	71	29	:	:	PUNCT
ejpam-6331	71	30	(	(	PUNCT
ejpam-6331	71	31	cifi-1	cifi-1	NUM
ejpam-6331	71	32	)	)	PUNCT
ejpam-6331	71	33	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	NOUN
ejpam-6331	71	34	)	)	PUNCT
ejpam-6331	71	35	≥	≥	NOUN
ejpam-6331	71	36	∅̃c(	∅̃c(	NOUN
ejpam-6331	71	37	⌜	⌜	NOUN
ejpam-6331	71	38	ϱ̃	ϱ̃	PROPN
ejpam-6331	71	39	⌝	⌝	PROPN
ejpam-6331	71	40	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	71	41	⌜	⌜	PROPN
ejpam-6331	71	42	ϱ̃	ϱ̃	PROPN
ejpam-6331	71	43	⌝	⌝	PROPN
ejpam-6331	71	44	)	)	PUNCT
ejpam-6331	71	45	,	,	PUNCT
ejpam-6331	71	46	φ̃c(0)e	φ̃c(0)e	NOUN
ejpam-6331	71	47	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	71	48	)	)	PUNCT
ejpam-6331	71	49	≤	≤	NOUN
ejpam-6331	71	50	φ̃c(	φ̃c(	NOUN
ejpam-6331	71	51	⌜	⌜	NOUN
ejpam-6331	71	52	ϱ̃	ϱ̃	PROPN
ejpam-6331	71	53	⌝	⌝	PROPN
ejpam-6331	71	54	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	71	55	⌜	⌜	PROPN
ejpam-6331	71	56	ϱ̃	ϱ̃	PROPN
ejpam-6331	71	57	⌝	⌝	PROPN
ejpam-6331	71	58	)	)	PUNCT
ejpam-6331	71	59	,	,	PUNCT
ejpam-6331	71	60	(	(	PUNCT
ejpam-6331	71	61	cifi-2	cifi-2	NOUN
ejpam-6331	71	62	)	)	PUNCT
ejpam-6331	71	63	∅̃c(	∅̃c(	NOUN
ejpam-6331	71	64	⌜	⌜	SYM
ejpam-6331	71	65	ϱ̃	ϱ̃	PROPN
ejpam-6331	71	66	⌝	⌝	PROPN
ejpam-6331	71	67	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	71	68	⌜	⌜	PROPN
ejpam-6331	71	69	ϱ̃	ϱ̃	PROPN
ejpam-6331	71	70	⌝	⌝	PROPN
ejpam-6331	71	71	)	)	PUNCT
ejpam-6331	71	72	≥	≥	NOUN
ejpam-6331	71	73	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	71	74	⌜	⌜	PROPN
ejpam-6331	71	75	ϱ̃	ϱ̃	PROPN
ejpam-6331	71	76	⌝	⌝	PROPN
ejpam-6331	71	77	∗	∗	NOUN
ejpam-6331	71	78	⌜	⌜	PROPN
ejpam-6331	71	79	ϑ̃	ϑ̃	PROPN
ejpam-6331	71	80	⌝	⌝	PROPN
ejpam-6331	71	81	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	71	82	⌜	⌜	PROPN
ejpam-6331	71	83	ϱ̃	ϱ̃	PROPN
ejpam-6331	71	84	⌝	⌝	PROPN
ejpam-6331	71	85	∗	∗	NOUN
ejpam-6331	71	86	⌜	⌜	PROPN
ejpam-6331	71	87	ϑ̃	ϑ̃	PROPN
ejpam-6331	71	88	⌝	⌝	PROPN
ejpam-6331	71	89	)	)	PUNCT
ejpam-6331	71	90	,	,	PUNCT
ejpam-6331	71	91	∅̃c(	∅̃c(	NOUN
ejpam-6331	71	92	⌜	⌜	SYM
ejpam-6331	71	93	ϑ̃	ϑ̃	PROPN
ejpam-6331	71	94	⌝	⌝	PROPN
ejpam-6331	71	95	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	71	96	⌜	⌜	PROPN
ejpam-6331	71	97	ϑ̃	ϑ̃	PROPN
ejpam-6331	71	98	⌝	⌝	PROPN
ejpam-6331	71	99	)	)	PUNCT
ejpam-6331	71	100	}	}	PUNCT
ejpam-6331	71	101	,	,	PUNCT
ejpam-6331	71	102	(	(	PUNCT
ejpam-6331	71	103	cifi-3	cifi-3	NOUN
ejpam-6331	71	104	)	)	PUNCT
ejpam-6331	71	105	φ̃c(	φ̃c(	NOUN
ejpam-6331	71	106	⌜	⌜	NOUN
ejpam-6331	71	107	ϱ̃	ϱ̃	PROPN
ejpam-6331	71	108	⌝	⌝	PROPN
ejpam-6331	71	109	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	71	110	⌜	⌜	PROPN
ejpam-6331	71	111	ϱ̃	ϱ̃	PROPN
ejpam-6331	71	112	⌝	⌝	PROPN
ejpam-6331	71	113	)	)	PUNCT
ejpam-6331	71	114	≤	≤	NOUN
ejpam-6331	71	115	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	72	1	⌜	⌜	PROPN
ejpam-6331	73	1	ϱ̃	ϱ̃	PROPN
ejpam-6331	73	2	⌝	⌝	PROPN
ejpam-6331	73	3	∗	∗	NOUN
ejpam-6331	73	4	⌜	⌜	PROPN
ejpam-6331	73	5	ϑ̃	ϑ̃	PROPN
ejpam-6331	73	6	⌝	⌝	PROPN
ejpam-6331	73	7	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	73	8	⌜	⌜	PROPN
ejpam-6331	73	9	ϱ̃	ϱ̃	PROPN
ejpam-6331	73	10	⌝	⌝	PROPN
ejpam-6331	73	11	∗	∗	NOUN
ejpam-6331	73	12	⌜	⌜	PROPN
ejpam-6331	73	13	ϑ̃	ϑ̃	PROPN
ejpam-6331	73	14	⌝	⌝	PROPN
ejpam-6331	73	15	)	)	PUNCT
ejpam-6331	73	16	,	,	PUNCT
ejpam-6331	73	17	φ̃c(	φ̃c(	PROPN
ejpam-6331	73	18	⌜	⌜	PROPN
ejpam-6331	73	19	ϑ̃	ϑ̃	PROPN
ejpam-6331	73	20	⌝	⌝	PROPN
ejpam-6331	73	21	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	73	22	⌜	⌜	PROPN
ejpam-6331	73	23	ϑ̃	ϑ̃	PROPN
ejpam-6331	73	24	⌝	⌝	PROPN
ejpam-6331	73	25	)	)	PUNCT
ejpam-6331	73	26	}	}	PUNCT
ejpam-6331	73	27	,	,	PUNCT
ejpam-6331	73	28	for	for	ADP
ejpam-6331	73	29	all	all	DET
ejpam-6331	73	30	⌜	⌜	PROPN
ejpam-6331	73	31	ϱ̃	ϱ̃	PROPN
ejpam-6331	73	32	⌝	⌝	PROPN
ejpam-6331	73	33	,	,	PUNCT
ejpam-6331	73	34	⌜	⌜	PROPN
ejpam-6331	73	35	ϑ̃	ϑ̃	PROPN
ejpam-6331	73	36	⌝	⌝	PROPN
ejpam-6331	73	37	∈	∈	PROPN
ejpam-6331	74	1	x	x	X
ejpam-6331	74	2	.	.	PUNCT
ejpam-6331	75	1	lemma	lemma	PROPN
ejpam-6331	75	2	1	1	X
ejpam-6331	75	3	.	.	PUNCT
ejpam-6331	76	1	let	let	VERB
ejpam-6331	76	2	c	c	PRON
ejpam-6331	76	3	be	be	AUX
ejpam-6331	76	4	a	a	DET
ejpam-6331	76	5	cif	cif	PROPN
ejpam-6331	76	6	-	-	PUNCT
ejpam-6331	76	7	ideal	ideal	NOUN
ejpam-6331	76	8	of	of	ADP
ejpam-6331	76	9	x	x	X
ejpam-6331	76	10	.	.	PUNCT
ejpam-6331	77	1	for	for	ADP
ejpam-6331	77	2	⌜	⌜	PROPN
ejpam-6331	77	3	ϱ̃	ϱ̃	PROPN
ejpam-6331	77	4	⌝	⌝	PROPN
ejpam-6331	77	5	,	,	PUNCT
ejpam-6331	77	6	⌜	⌜	PROPN
ejpam-6331	77	7	ϑ̃	ϑ̃	PROPN
ejpam-6331	77	8	⌝	⌝	PROPN
ejpam-6331	77	9	∈	∈	PROPN
ejpam-6331	77	10	x	x	PUNCT
ejpam-6331	77	11	with	with	ADP
ejpam-6331	77	12	⌜	⌜	NOUN
ejpam-6331	77	13	ϱ̃	ϱ̃	PROPN
ejpam-6331	77	14	⌝	⌝	PROPN
ejpam-6331	77	15	≤	≤	NOUN
ejpam-6331	77	16	⌜	⌜	PROPN
ejpam-6331	77	17	ϑ̃	ϑ̃	PROPN
ejpam-6331	77	18	⌝	⌝	PROPN
ejpam-6331	77	19	holds	hold	VERB
ejpam-6331	77	20	in	in	ADP
ejpam-6331	77	21	x	x	X
ejpam-6331	77	22	.	.	PUNCT
ejpam-6331	78	1	the	the	DET
ejpam-6331	78	2	following	follow	VERB
ejpam-6331	78	3	are	be	AUX
ejpam-6331	78	4	equivalent	equivalent	ADJ
ejpam-6331	78	5	:	:	PUNCT
ejpam-6331	78	6	(	(	PUNCT
ejpam-6331	78	7	1	1	NUM
ejpam-6331	78	8	)	)	PUNCT
ejpam-6331	78	9	∅̃c(	∅̃c(	NOUN
ejpam-6331	78	10	⌜	⌜	PROPN
ejpam-6331	78	11	ϱ̃	ϱ̃	PROPN
ejpam-6331	78	12	⌝	⌝	PROPN
ejpam-6331	78	13	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	78	14	⌜	⌜	PROPN
ejpam-6331	78	15	ϱ̃	ϱ̃	PROPN
ejpam-6331	78	16	⌝	⌝	PROPN
ejpam-6331	78	17	)	)	PUNCT
ejpam-6331	78	18	≥	≥	NOUN
ejpam-6331	78	19	∅̃c(	∅̃c(	NOUN
ejpam-6331	78	20	⌜	⌜	SYM
ejpam-6331	78	21	ϑ̃	ϑ̃	PROPN
ejpam-6331	78	22	⌝	⌝	PROPN
ejpam-6331	78	23	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	78	24	⌜	⌜	PROPN
ejpam-6331	78	25	ϑ̃	ϑ̃	PROPN
ejpam-6331	78	26	⌝	⌝	PROPN
ejpam-6331	78	27	)	)	PUNCT
ejpam-6331	78	28	,	,	PUNCT
ejpam-6331	78	29	φ̃c(	φ̃c(	VERB
ejpam-6331	78	30	⌜	⌜	NOUN
ejpam-6331	78	31	ϱ̃	ϱ̃	PROPN
ejpam-6331	78	32	⌝	⌝	PROPN
ejpam-6331	78	33	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	78	34	⌜	⌜	PROPN
ejpam-6331	78	35	ϱ̃	ϱ̃	PROPN
ejpam-6331	78	36	⌝	⌝	PROPN
ejpam-6331	78	37	)	)	PUNCT
ejpam-6331	78	38	≤	≤	NOUN
ejpam-6331	78	39	φ̃c(	φ̃c(	PROPN
ejpam-6331	78	40	⌜	⌜	PROPN
ejpam-6331	78	41	ϑ̃	ϑ̃	PROPN
ejpam-6331	78	42	⌝	⌝	PROPN
ejpam-6331	78	43	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	78	44	⌜	⌜	PROPN
ejpam-6331	78	45	ϑ̃	ϑ̃	PROPN
ejpam-6331	78	46	⌝	⌝	PROPN
ejpam-6331	78	47	)	)	PUNCT
ejpam-6331	78	48	,	,	PUNCT
ejpam-6331	78	49	(	(	PUNCT
ejpam-6331	78	50	2	2	X
ejpam-6331	78	51	)	)	PUNCT
ejpam-6331	78	52	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	NOUN
ejpam-6331	78	53	)	)	PUNCT
ejpam-6331	79	1	=	=	PUNCT
ejpam-6331	79	2	∅̃c(	∅̃c(	NOUN
ejpam-6331	79	3	⌜	⌜	NOUN
ejpam-6331	79	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	79	5	⌝	⌝	PROPN
ejpam-6331	79	6	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	79	7	⌜	⌜	PROPN
ejpam-6331	79	8	ϱ̃	ϱ̃	PROPN
ejpam-6331	79	9	⌝	⌝	PROPN
ejpam-6331	79	10	)	)	PUNCT
ejpam-6331	79	11	,	,	PUNCT
ejpam-6331	79	12	φ̃c(0)e	φ̃c(0)e	NOUN
ejpam-6331	79	13	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	79	14	)	)	PUNCT
ejpam-6331	79	15	=	=	PUNCT
ejpam-6331	80	1	φ̃c(	φ̃c(	NOUN
ejpam-6331	80	2	⌜	⌜	NOUN
ejpam-6331	80	3	ϱ̃	ϱ̃	PROPN
ejpam-6331	80	4	⌝	⌝	PROPN
ejpam-6331	80	5	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	80	6	⌜	⌜	PROPN
ejpam-6331	80	7	ϱ̃	ϱ̃	PROPN
ejpam-6331	80	8	⌝	⌝	PROPN
ejpam-6331	80	9	)	)	PUNCT
ejpam-6331	80	10	.	.	PUNCT
ejpam-6331	81	1	proof	proof	NOUN
ejpam-6331	81	2	.	.	PUNCT
ejpam-6331	82	1	straightforward	straightforward	ADJ
ejpam-6331	82	2	.	.	PUNCT
ejpam-6331	83	1	definition	definition	NOUN
ejpam-6331	83	2	7	7	NUM
ejpam-6331	83	3	.	.	PUNCT
ejpam-6331	84	1	a	a	DET
ejpam-6331	84	2	cif	cif	PROPN
ejpam-6331	84	3	-	-	PUNCT
ejpam-6331	84	4	set	set	VERB
ejpam-6331	84	5	c	c	NOUN
ejpam-6331	84	6	=	=	SYM
ejpam-6331	84	7	(	(	PUNCT
ejpam-6331	84	8	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	84	9	,	,	PUNCT
ejpam-6331	84	10	φ̃ce	φ̃ce	PROPN
ejpam-6331	84	11	iθ̃c	iθ̃c	PROPN
ejpam-6331	84	12	)	)	PUNCT
ejpam-6331	84	13	forms	form	VERB
ejpam-6331	84	14	a	a	DET
ejpam-6331	84	15	complex	complex	ADJ
ejpam-6331	84	16	intuitionistic	intuitionistic	ADJ
ejpam-6331	84	17	fuzzy	fuzzy	ADJ
ejpam-6331	84	18	quasiassociative	quasiassociative	ADJ
ejpam-6331	84	19	ideal	ideal	NOUN
ejpam-6331	84	20	(	(	PUNCT
ejpam-6331	84	21	cifqa	cifqa	NOUN
ejpam-6331	84	22	-	-	PUNCT
ejpam-6331	84	23	ideal	ideal	NOUN
ejpam-6331	84	24	)	)	PUNCT
ejpam-6331	84	25	of	of	ADP
ejpam-6331	84	26	x	x	PRON
ejpam-6331	84	27	if	if	SCONJ
ejpam-6331	84	28	it	it	PRON
ejpam-6331	84	29	satisfies	satisfy	VERB
ejpam-6331	84	30	the	the	DET
ejpam-6331	84	31	following	following	NOUN
ejpam-6331	84	32	:	:	PUNCT
ejpam-6331	84	33	(	(	PUNCT
ejpam-6331	84	34	cifqai-1	cifqai-1	NUM
ejpam-6331	84	35	)	)	PUNCT
ejpam-6331	84	36	∅̃c(	∅̃c(	NOUN
ejpam-6331	84	37	⌜	⌜	NOUN
ejpam-6331	84	38	ϱ̃	ϱ̃	PROPN
ejpam-6331	84	39	⌝	⌝	PROPN
ejpam-6331	84	40	∗	∗	NOUN
ejpam-6331	84	41	⌜	⌜	PROPN
ejpam-6331	84	42	κ̃	κ̃	PROPN
ejpam-6331	84	43	⌝	⌝	PROPN
ejpam-6331	84	44	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	84	45	⌜	⌜	PROPN
ejpam-6331	84	46	ϱ̃	ϱ̃	PROPN
ejpam-6331	84	47	⌝	⌝	PROPN
ejpam-6331	84	48	∗	∗	NOUN
ejpam-6331	84	49	⌜	⌜	PROPN
ejpam-6331	84	50	κ̃	κ̃	PROPN
ejpam-6331	84	51	⌝	⌝	PROPN
ejpam-6331	84	52	)	)	PUNCT
ejpam-6331	84	53	≥	≥	NOUN
ejpam-6331	84	54	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	84	55	⌜	⌜	PROPN
ejpam-6331	84	56	ϱ̃	ϱ̃	PROPN
ejpam-6331	84	57	⌝	⌝	PROPN
ejpam-6331	84	58	∗	∗	NOUN
ejpam-6331	84	59	(	(	PUNCT
ejpam-6331	84	60	⌜	⌜	PROPN
ejpam-6331	84	61	ϑ̃	ϑ̃	PROPN
ejpam-6331	84	62	⌝	⌝	PROPN
ejpam-6331	84	63	∗	∗	NOUN
ejpam-6331	84	64	⌜	⌜	PROPN
ejpam-6331	84	65	κ̃	κ̃	PROPN
ejpam-6331	84	66	⌝	⌝	PROPN
ejpam-6331	84	67	))eiω̃c(	))eiω̃c(	PROPN
ejpam-6331	84	68	⌜	⌜	PROPN
ejpam-6331	84	69	ϱ̃	ϱ̃	PROPN
ejpam-6331	84	70	⌝	⌝	PROPN
ejpam-6331	84	71	∗(	∗(	NOUN
ejpam-6331	84	72	⌜	⌜	PROPN
ejpam-6331	84	73	ϑ̃	ϑ̃	PROPN
ejpam-6331	84	74	⌝	⌝	PROPN
ejpam-6331	84	75	∗	∗	NOUN
ejpam-6331	84	76	⌜	⌜	PROPN
ejpam-6331	84	77	κ̃	κ̃	PROPN
ejpam-6331	84	78	⌝	⌝	PROPN
ejpam-6331	84	79	)	)	PUNCT
ejpam-6331	84	80	)	)	PUNCT
ejpam-6331	84	81	,	,	PUNCT
ejpam-6331	84	82	∅̃c(	∅̃c(	NOUN
ejpam-6331	84	83	⌜	⌜	SYM
ejpam-6331	84	84	ϑ̃	ϑ̃	PROPN
ejpam-6331	84	85	⌝	⌝	PROPN
ejpam-6331	84	86	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	84	87	⌜	⌜	PROPN
ejpam-6331	84	88	ϑ̃	ϑ̃	PROPN
ejpam-6331	84	89	⌝	⌝	PROPN
ejpam-6331	84	90	)	)	PUNCT
ejpam-6331	84	91	}	}	PUNCT
ejpam-6331	84	92	,	,	PUNCT
ejpam-6331	84	93	(	(	PUNCT
ejpam-6331	84	94	cifqai-2	cifqai-2	NOUN
ejpam-6331	84	95	)	)	PUNCT
ejpam-6331	84	96	φ̃c(	φ̃c(	NOUN
ejpam-6331	84	97	⌜	⌜	NOUN
ejpam-6331	84	98	ϱ̃	ϱ̃	PROPN
ejpam-6331	84	99	⌝	⌝	PROPN
ejpam-6331	84	100	∗	∗	NOUN
ejpam-6331	84	101	⌜	⌜	PROPN
ejpam-6331	84	102	κ̃	κ̃	PROPN
ejpam-6331	84	103	⌝	⌝	PROPN
ejpam-6331	84	104	)eiθ̃c(	)eiθ̃c(	ADJ
ejpam-6331	84	105	⌜	⌜	PROPN
ejpam-6331	84	106	ϱ̃	ϱ̃	PROPN
ejpam-6331	84	107	⌝	⌝	PROPN
ejpam-6331	84	108	∗	∗	NOUN
ejpam-6331	84	109	⌜	⌜	PROPN
ejpam-6331	84	110	κ̃	κ̃	PROPN
ejpam-6331	84	111	⌝	⌝	PROPN
ejpam-6331	84	112	)	)	PUNCT
ejpam-6331	84	113	≤	≤	NOUN
ejpam-6331	84	114	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	84	115	⌜	⌜	PROPN
ejpam-6331	84	116	ϱ̃	ϱ̃	PROPN
ejpam-6331	84	117	⌝	⌝	PROPN
ejpam-6331	84	118	∗	∗	NOUN
ejpam-6331	84	119	(	(	PUNCT
ejpam-6331	84	120	⌜	⌜	PROPN
ejpam-6331	84	121	ϑ̃	ϑ̃	PROPN
ejpam-6331	84	122	⌝	⌝	PROPN
ejpam-6331	84	123	∗	∗	NOUN
ejpam-6331	84	124	⌜	⌜	PROPN
ejpam-6331	84	125	κ̃	κ̃	PROPN
ejpam-6331	84	126	⌝	⌝	PROPN
ejpam-6331	84	127	))eiθ̃c(	))eiθ̃c(	DET
ejpam-6331	84	128	⌜	⌜	PROPN
ejpam-6331	84	129	ϱ̃	ϱ̃	PROPN
ejpam-6331	84	130	⌝	⌝	PROPN
ejpam-6331	84	131	∗(	∗(	NOUN
ejpam-6331	84	132	⌜	⌜	PROPN
ejpam-6331	84	133	ϑ̃	ϑ̃	PROPN
ejpam-6331	84	134	⌝	⌝	PROPN
ejpam-6331	84	135	∗	∗	NOUN
ejpam-6331	84	136	⌜	⌜	PROPN
ejpam-6331	84	137	κ̃	κ̃	PROPN
ejpam-6331	84	138	⌝	⌝	PROPN
ejpam-6331	84	139	)	)	PUNCT
ejpam-6331	84	140	)	)	PUNCT
ejpam-6331	84	141	,	,	PUNCT
ejpam-6331	84	142	φ̃c(	φ̃c(	PROPN
ejpam-6331	84	143	⌜	⌜	PROPN
ejpam-6331	84	144	ϑ̃	ϑ̃	PROPN
ejpam-6331	84	145	⌝	⌝	PROPN
ejpam-6331	84	146	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	84	147	⌜	⌜	PROPN
ejpam-6331	84	148	ϑ̃	ϑ̃	PROPN
ejpam-6331	84	149	⌝	⌝	PROPN
ejpam-6331	84	150	)	)	PUNCT
ejpam-6331	84	151	}	}	PUNCT
ejpam-6331	84	152	,	,	PUNCT
ejpam-6331	84	153	for	for	ADP
ejpam-6331	84	154	all	all	DET
ejpam-6331	84	155	⌜	⌜	PROPN
ejpam-6331	84	156	ϱ̃	ϱ̃	PROPN
ejpam-6331	84	157	⌝	⌝	PROPN
ejpam-6331	84	158	,	,	PUNCT
ejpam-6331	84	159	⌜	⌜	PROPN
ejpam-6331	84	160	ϑ̃	ϑ̃	PROPN
ejpam-6331	84	161	⌝	⌝	PROPN
ejpam-6331	84	162	,	,	PUNCT
ejpam-6331	84	163	⌜	⌜	PROPN
ejpam-6331	84	164	κ̃	κ̃	PROPN
ejpam-6331	84	165	⌝	⌝	PROPN
ejpam-6331	84	166	∈	∈	PROPN
ejpam-6331	84	167	x	x	X
ejpam-6331	84	168	.	.	PUNCT
ejpam-6331	84	169	example	example	NOUN
ejpam-6331	85	1	2	2	NUM
ejpam-6331	85	2	.	.	PUNCT
ejpam-6331	85	3	let	let	VERB
ejpam-6331	85	4	x	x	PUNCT
ejpam-6331	85	5	=	=	PUNCT
ejpam-6331	85	6	{	{	PUNCT
ejpam-6331	85	7	0	0	NUM
ejpam-6331	85	8	,	,	PUNCT
ejpam-6331	85	9	τ̃	τ̃	PROPN
ejpam-6331	85	10	,	,	PUNCT
ejpam-6331	85	11	υ̃	υ̃	PROPN
ejpam-6331	85	12	,	,	PUNCT
ejpam-6331	85	13	ζ̃	ζ̃	PROPN
ejpam-6331	85	14	}	}	PUNCT
ejpam-6331	85	15	be	be	AUX
ejpam-6331	85	16	a	a	DET
ejpam-6331	85	17	bci	bci	NOUN
ejpam-6331	85	18	-	-	NOUN
ejpam-6331	85	19	algebra	algebra	NOUN
ejpam-6331	85	20	with	with	ADP
ejpam-6331	85	21	cayley	cayley	ADJ
ejpam-6331	85	22	table	table	NOUN
ejpam-6331	85	23	1	1	NUM
ejpam-6331	85	24	.	.	PUNCT
ejpam-6331	86	1	let	let	VERB
ejpam-6331	86	2	c	c	NOUN
ejpam-6331	86	3	=	=	SYM
ejpam-6331	86	4	(	(	PUNCT
ejpam-6331	86	5	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	86	6	,	,	PUNCT
ejpam-6331	86	7	φ̃ce	φ̃ce	PROPN
ejpam-6331	86	8	iθ̃c	iθ̃c	PROPN
ejpam-6331	86	9	)	)	PUNCT
ejpam-6331	86	10	table	table	NOUN
ejpam-6331	86	11	1	1	NUM
ejpam-6331	86	12	:	:	PUNCT
ejpam-6331	86	13	cayley	cayley	ADJ
ejpam-6331	86	14	table	table	NOUN
ejpam-6331	86	15	for	for	ADP
ejpam-6331	86	16	(	(	PUNCT
ejpam-6331	86	17	x	x	INTJ
ejpam-6331	86	18	,	,	PUNCT
ejpam-6331	86	19	∗	∗	NOUN
ejpam-6331	86	20	)	)	PUNCT
ejpam-6331	86	21	*	*	PUNCT
ejpam-6331	86	22	0	0	PUNCT
ejpam-6331	87	1	τ̃	τ̃	PROPN
ejpam-6331	87	2	υ̃	υ̃	PROPN
ejpam-6331	87	3	ζ̃	ζ̃	PROPN
ejpam-6331	87	4	0	0	NUM
ejpam-6331	87	5	0	0	X
ejpam-6331	88	1	τ̃	τ̃	PROPN
ejpam-6331	88	2	υ̃	υ̃	PROPN
ejpam-6331	88	3	ζ̃	ζ̃	PROPN
ejpam-6331	88	4	τ̃	τ̃	PROPN
ejpam-6331	88	5	τ̃	τ̃	PROPN
ejpam-6331	88	6	0	0	NUM
ejpam-6331	88	7	ζ̃	ζ̃	PROPN
ejpam-6331	88	8	υ̃	υ̃	PROPN
ejpam-6331	88	9	υ̃	υ̃	PROPN
ejpam-6331	89	1	υ̃	υ̃	PROPN
ejpam-6331	89	2	ζ̃	ζ̃	PROPN
ejpam-6331	89	3	0	0	PUNCT
ejpam-6331	90	1	τ̃	τ̃	PROPN
ejpam-6331	90	2	ζ̃	ζ̃	PROPN
ejpam-6331	90	3	ζ̃	ζ̃	PROPN
ejpam-6331	90	4	υ̃	υ̃	PROPN
ejpam-6331	90	5	τ̃	τ̃	PROPN
ejpam-6331	90	6	0	0	NUM
ejpam-6331	90	7	be	be	AUX
ejpam-6331	90	8	a	a	DET
ejpam-6331	90	9	cif	cif	PROPN
ejpam-6331	90	10	-	-	PUNCT
ejpam-6331	90	11	set	set	PROPN
ejpam-6331	90	12	is	be	AUX
ejpam-6331	90	13	given	give	VERB
ejpam-6331	90	14	by	by	ADP
ejpam-6331	90	15	table	table	NOUN
ejpam-6331	90	16	2	2	NUM
ejpam-6331	90	17	.	.	PUNCT
ejpam-6331	90	18	t.	t.	PROPN
ejpam-6331	90	19	ramesh	ramesh	PROPN
ejpam-6331	90	20	,	,	PUNCT
ejpam-6331	90	21	m.	m.	NOUN
ejpam-6331	90	22	balamurugan	balamurugan	PROPN
ejpam-6331	90	23	,	,	PUNCT
ejpam-6331	90	24	a.	a.	NOUN
ejpam-6331	90	25	iampan	iampan	PROPN
ejpam-6331	90	26	/	/	SYM
ejpam-6331	90	27	eur	eur	PROPN
ejpam-6331	90	28	.	.	PUNCT
ejpam-6331	91	1	j.	j.	PROPN
ejpam-6331	91	2	pure	pure	PROPN
ejpam-6331	91	3	appl	appl	PROPN
ejpam-6331	91	4	.	.	PROPN
ejpam-6331	91	5	math	math	PROPN
ejpam-6331	91	6	,	,	PUNCT
ejpam-6331	91	7	18	18	NUM
ejpam-6331	91	8	(	(	PUNCT
ejpam-6331	91	9	3	3	NUM
ejpam-6331	91	10	)	)	PUNCT
ejpam-6331	91	11	(	(	PUNCT
ejpam-6331	91	12	2025	2025	NUM
ejpam-6331	91	13	)	)	PUNCT
ejpam-6331	91	14	,	,	PUNCT
ejpam-6331	91	15	6331	6331	NUM
ejpam-6331	91	16	5	5	NUM
ejpam-6331	91	17	of	of	ADP
ejpam-6331	91	18	14	14	NUM
ejpam-6331	91	19	table	table	NOUN
ejpam-6331	91	20	2	2	NUM
ejpam-6331	91	21	:	:	PUNCT
ejpam-6331	91	22	the	the	DET
ejpam-6331	91	23	values	value	NOUN
ejpam-6331	91	24	of	of	ADP
ejpam-6331	91	25	(	(	PUNCT
ejpam-6331	91	26	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	91	27	,	,	PUNCT
ejpam-6331	91	28	φ̃ce	φ̃ce	PROPN
ejpam-6331	91	29	iθ̃c	iθ̃c	PROPN
ejpam-6331	91	30	)	)	PUNCT
ejpam-6331	91	31	x	x	X
ejpam-6331	91	32	∅̃ceiω̃c	∅̃ceiω̃c	PUNCT
ejpam-6331	91	33	φ̃ce	φ̃ce	VERB
ejpam-6331	91	34	iθ̃c	iθ̃c	NOUN
ejpam-6331	91	35	0	0	NUM
ejpam-6331	91	36	0.7e	0.7e	NOUN
ejpam-6331	91	37	iπ	iπ	ADV
ejpam-6331	91	38	3	3	NUM
ejpam-6331	91	39	0.2e	0.2e	NOUN
ejpam-6331	91	40	iπ	iπ	ADV
ejpam-6331	91	41	2	2	NUM
ejpam-6331	91	42	τ̃	τ̃	NOUN
ejpam-6331	91	43	0.5e	0.5e	NUM
ejpam-6331	91	44	iπ	iπ	ADV
ejpam-6331	91	45	4	4	NUM
ejpam-6331	91	46	0.3e	0.3e	NOUN
ejpam-6331	91	47	iπ	iπ	PRON
ejpam-6331	91	48	3	3	NUM
ejpam-6331	91	49	υ̃	υ̃	PROPN
ejpam-6331	91	50	0.3e	0.3e	VERB
ejpam-6331	91	51	iπ	iπ	ADV
ejpam-6331	91	52	3	3	NUM
ejpam-6331	91	53	0.5e	0.5e	NUM
ejpam-6331	91	54	iπ	iπ	ADV
ejpam-6331	91	55	4	4	NUM
ejpam-6331	91	56	ζ̃	ζ̃	PROPN
ejpam-6331	91	57	0.3e	0.3e	NOUN
ejpam-6331	91	58	iπ	iπ	ADV
ejpam-6331	91	59	5	5	NUM
ejpam-6331	91	60	0.3e	0.3e	NOUN
ejpam-6331	91	61	iπ	iπ	ADV
ejpam-6331	91	62	3	3	NUM
ejpam-6331	91	63	our	our	PRON
ejpam-6331	91	64	calculations	calculation	NOUN
ejpam-6331	91	65	demonstrate	demonstrate	VERB
ejpam-6331	91	66	that	that	SCONJ
ejpam-6331	91	67	c	c	PROPN
ejpam-6331	91	68	is	be	AUX
ejpam-6331	91	69	a	a	DET
ejpam-6331	91	70	cifqa	cifqa	NOUN
ejpam-6331	91	71	-	-	PUNCT
ejpam-6331	91	72	ideal	ideal	NOUN
ejpam-6331	91	73	in	in	ADP
ejpam-6331	91	74	x	x	PROPN
ejpam-6331	91	75	.	.	PUNCT
ejpam-6331	92	1	theorem	theorem	NOUN
ejpam-6331	92	2	1	1	NUM
ejpam-6331	92	3	.	.	PUNCT
ejpam-6331	93	1	in	in	ADP
ejpam-6331	93	2	a	a	DET
ejpam-6331	93	3	bci	bci	NOUN
ejpam-6331	93	4	-	-	NOUN
ejpam-6331	93	5	algebra	algebra	NOUN
ejpam-6331	93	6	,	,	PUNCT
ejpam-6331	93	7	every	every	DET
ejpam-6331	93	8	cifqa	cifqa	NOUN
ejpam-6331	93	9	-	-	PUNCT
ejpam-6331	93	10	ideal	ideal	NOUN
ejpam-6331	93	11	is	be	AUX
ejpam-6331	93	12	necessarily	necessarily	ADV
ejpam-6331	93	13	a	a	DET
ejpam-6331	93	14	cif	cif	PROPN
ejpam-6331	93	15	-	-	PUNCT
ejpam-6331	93	16	ideal	ideal	NOUN
ejpam-6331	93	17	.	.	PUNCT
ejpam-6331	94	1	proof	proof	NOUN
ejpam-6331	94	2	.	.	PUNCT
ejpam-6331	95	1	let	let	VERB
ejpam-6331	95	2	c	c	NOUN
ejpam-6331	95	3	=	=	SYM
ejpam-6331	95	4	(	(	PUNCT
ejpam-6331	95	5	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	95	6	,	,	PUNCT
ejpam-6331	95	7	φ̃ce	φ̃ce	PROPN
ejpam-6331	95	8	iθ̃c	iθ̃c	PROPN
ejpam-6331	95	9	)	)	PUNCT
ejpam-6331	95	10	be	be	VERB
ejpam-6331	95	11	a	a	DET
ejpam-6331	95	12	cifqa	cifqa	NOUN
ejpam-6331	95	13	-	-	PUNCT
ejpam-6331	95	14	ideal	ideal	NOUN
ejpam-6331	95	15	of	of	ADP
ejpam-6331	95	16	x	x	X
ejpam-6331	95	17	.	.	PUNCT
ejpam-6331	96	1	put	put	VERB
ejpam-6331	96	2	⌜	⌜	PROPN
ejpam-6331	96	3	κ̃	κ̃	PROPN
ejpam-6331	96	4	⌝	⌝	PROPN
ejpam-6331	96	5	=	=	SYM
ejpam-6331	96	6	0	0	NUM
ejpam-6331	97	1	in	in	ADP
ejpam-6331	97	2	definition	definition	NOUN
ejpam-6331	97	3	7	7	NUM
ejpam-6331	97	4	,	,	PUNCT
ejpam-6331	97	5	cifqai-2	cifqai-2	NUM
ejpam-6331	97	6	and	and	CCONJ
ejpam-6331	97	7	cifqai-3	cifqai-3	NUM
ejpam-6331	97	8	,	,	PUNCT
ejpam-6331	97	9	we	we	PRON
ejpam-6331	97	10	have	have	VERB
ejpam-6331	97	11	∅̃c(	∅̃c(	NOUN
ejpam-6331	97	12	⌜	⌜	NOUN
ejpam-6331	97	13	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	14	⌝	⌝	PROPN
ejpam-6331	97	15	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	97	16	⌜	⌜	PROPN
ejpam-6331	97	17	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	18	⌝	⌝	PROPN
ejpam-6331	97	19	)	)	PUNCT
ejpam-6331	97	20	=	=	SYM
ejpam-6331	97	21	∅̃c(	∅̃c(	NOUN
ejpam-6331	97	22	⌜	⌜	NOUN
ejpam-6331	97	23	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	24	⌝	⌝	PROPN
ejpam-6331	97	25	∗	∗	NOUN
ejpam-6331	97	26	0)eiω̃c(	0)eiω̃c(	NUM
ejpam-6331	97	27	⌜	⌜	NOUN
ejpam-6331	97	28	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	29	⌝	⌝	PROPN
ejpam-6331	97	30	∗0	∗0	PROPN
ejpam-6331	97	31	)	)	PUNCT
ejpam-6331	97	32	≥	≥	NOUN
ejpam-6331	97	33	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	97	34	⌜	⌜	PROPN
ejpam-6331	97	35	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	36	⌝	⌝	PROPN
ejpam-6331	97	37	∗	∗	NOUN
ejpam-6331	97	38	(	(	PUNCT
ejpam-6331	97	39	⌜	⌜	PROPN
ejpam-6331	97	40	ϑ̃	ϑ̃	PROPN
ejpam-6331	97	41	⌝	⌝	PROPN
ejpam-6331	97	42	∗	∗	NOUN
ejpam-6331	97	43	0))eiω̃c(	0))eiω̃c(	NOUN
ejpam-6331	97	44	⌜	⌜	NOUN
ejpam-6331	97	45	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	46	⌝	⌝	PROPN
ejpam-6331	97	47	∗(	∗(	NOUN
ejpam-6331	97	48	⌜	⌜	PROPN
ejpam-6331	97	49	ϑ̃	ϑ̃	PROPN
ejpam-6331	97	50	⌝	⌝	PROPN
ejpam-6331	97	51	∗0	∗0	PROPN
ejpam-6331	97	52	)	)	PUNCT
ejpam-6331	97	53	)	)	PUNCT
ejpam-6331	97	54	,	,	PUNCT
ejpam-6331	97	55	∅̃c(	∅̃c(	NOUN
ejpam-6331	97	56	⌜	⌜	SYM
ejpam-6331	97	57	ϑ̃	ϑ̃	PROPN
ejpam-6331	97	58	⌝	⌝	PROPN
ejpam-6331	97	59	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	97	60	⌜	⌜	PROPN
ejpam-6331	97	61	ϑ̃	ϑ̃	PROPN
ejpam-6331	97	62	⌝	⌝	PROPN
ejpam-6331	97	63	)	)	PUNCT
ejpam-6331	97	64	}	}	PUNCT
ejpam-6331	97	65	∅̃c(	∅̃c(	NOUN
ejpam-6331	97	66	⌜	⌜	PROPN
ejpam-6331	97	67	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	68	⌝	⌝	PROPN
ejpam-6331	97	69	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	97	70	⌜	⌜	PROPN
ejpam-6331	97	71	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	72	⌝	⌝	PROPN
ejpam-6331	97	73	)	)	PUNCT
ejpam-6331	97	74	≥	≥	NOUN
ejpam-6331	97	75	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	97	76	⌜	⌜	PROPN
ejpam-6331	97	77	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	78	⌝	⌝	PROPN
ejpam-6331	97	79	∗	∗	NOUN
ejpam-6331	97	80	⌜	⌜	PROPN
ejpam-6331	97	81	ϑ̃	ϑ̃	PROPN
ejpam-6331	97	82	⌝	⌝	PROPN
ejpam-6331	97	83	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	97	84	⌜	⌜	PROPN
ejpam-6331	97	85	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	86	⌝	⌝	PROPN
ejpam-6331	97	87	∗	∗	NOUN
ejpam-6331	97	88	⌜	⌜	PROPN
ejpam-6331	97	89	ϑ̃	ϑ̃	PROPN
ejpam-6331	97	90	⌝	⌝	PROPN
ejpam-6331	97	91	)	)	PUNCT
ejpam-6331	97	92	,	,	PUNCT
ejpam-6331	97	93	∅̃c(	∅̃c(	NOUN
ejpam-6331	97	94	⌜	⌜	SYM
ejpam-6331	97	95	ϑ̃	ϑ̃	PROPN
ejpam-6331	97	96	⌝	⌝	PROPN
ejpam-6331	97	97	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	97	98	⌜	⌜	PROPN
ejpam-6331	97	99	ϑ̃	ϑ̃	PROPN
ejpam-6331	97	100	⌝	⌝	PROPN
ejpam-6331	97	101	)	)	PUNCT
ejpam-6331	97	102	}	}	PUNCT
ejpam-6331	97	103	,	,	PUNCT
ejpam-6331	97	104	and	and	CCONJ
ejpam-6331	97	105	φ̃c(	φ̃c(	PROPN
ejpam-6331	97	106	⌜	⌜	NOUN
ejpam-6331	97	107	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	108	⌝	⌝	PROPN
ejpam-6331	97	109	)e	)e	NOUN
ejpam-6331	97	110	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	97	111	⌜	⌜	PROPN
ejpam-6331	97	112	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	113	⌝	⌝	PROPN
ejpam-6331	97	114	)	)	PUNCT
ejpam-6331	97	115	=	=	PUNCT
ejpam-6331	97	116	φ̃c(	φ̃c(	PROPN
ejpam-6331	97	117	⌜	⌜	NOUN
ejpam-6331	97	118	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	119	⌝	⌝	PROPN
ejpam-6331	97	120	∗	∗	NOUN
ejpam-6331	97	121	0)eiθ̃c(	0)eiθ̃c(	NUM
ejpam-6331	97	122	⌜	⌜	PROPN
ejpam-6331	97	123	ϱ̃	ϱ̃	PROPN
ejpam-6331	97	124	⌝	⌝	PROPN
ejpam-6331	97	125	∗0	∗0	PROPN
ejpam-6331	97	126	)	)	PUNCT
ejpam-6331	97	127	≤	≤	NOUN
ejpam-6331	97	128	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	98	1	⌜	⌜	PROPN
ejpam-6331	98	2	ϱ̃	ϱ̃	PROPN
ejpam-6331	98	3	⌝	⌝	PROPN
ejpam-6331	98	4	∗	∗	NOUN
ejpam-6331	98	5	(	(	PUNCT
ejpam-6331	98	6	⌜	⌜	PROPN
ejpam-6331	98	7	ϑ̃	ϑ̃	PROPN
ejpam-6331	98	8	⌝	⌝	PROPN
ejpam-6331	98	9	∗	∗	NOUN
ejpam-6331	98	10	0))eiθ̃c(	0))eiθ̃c(	PUNCT
ejpam-6331	98	11	⌜	⌜	PROPN
ejpam-6331	98	12	ϱ̃	ϱ̃	PROPN
ejpam-6331	98	13	⌝	⌝	PROPN
ejpam-6331	98	14	∗(	∗(	NOUN
ejpam-6331	98	15	⌜	⌜	PROPN
ejpam-6331	98	16	ϑ̃	ϑ̃	PROPN
ejpam-6331	98	17	⌝	⌝	PROPN
ejpam-6331	98	18	∗0	∗0	PROPN
ejpam-6331	98	19	)	)	PUNCT
ejpam-6331	98	20	)	)	PUNCT
ejpam-6331	98	21	,	,	PUNCT
ejpam-6331	98	22	φ̃c(	φ̃c(	PROPN
ejpam-6331	98	23	⌜	⌜	PROPN
ejpam-6331	98	24	ϑ̃	ϑ̃	PROPN
ejpam-6331	98	25	⌝	⌝	PROPN
ejpam-6331	98	26	)e	)e	NOUN
ejpam-6331	98	27	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	98	28	⌜	⌜	PROPN
ejpam-6331	98	29	ϑ̃	ϑ̃	PROPN
ejpam-6331	98	30	⌝	⌝	PROPN
ejpam-6331	98	31	)	)	PUNCT
ejpam-6331	98	32	}	}	PUNCT
ejpam-6331	98	33	φ̃c(	φ̃c(	VERB
ejpam-6331	98	34	⌜	⌜	NOUN
ejpam-6331	98	35	ϱ̃	ϱ̃	PROPN
ejpam-6331	98	36	⌝	⌝	PROPN
ejpam-6331	98	37	)e	)e	NOUN
ejpam-6331	98	38	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	98	39	⌜	⌜	PROPN
ejpam-6331	98	40	ϱ̃	ϱ̃	PROPN
ejpam-6331	98	41	⌝	⌝	PROPN
ejpam-6331	98	42	)	)	PUNCT
ejpam-6331	98	43	≤	≤	NOUN
ejpam-6331	98	44	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	98	45	⌜	⌜	PROPN
ejpam-6331	98	46	ϱ̃	ϱ̃	PROPN
ejpam-6331	98	47	⌝	⌝	PROPN
ejpam-6331	98	48	∗	∗	NOUN
ejpam-6331	98	49	⌜	⌜	PROPN
ejpam-6331	98	50	ϑ̃	ϑ̃	PROPN
ejpam-6331	98	51	⌝	⌝	PROPN
ejpam-6331	98	52	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	98	53	⌜	⌜	PROPN
ejpam-6331	98	54	ϱ̃	ϱ̃	PROPN
ejpam-6331	98	55	⌝	⌝	PROPN
ejpam-6331	98	56	∗	∗	NOUN
ejpam-6331	98	57	⌜	⌜	PROPN
ejpam-6331	98	58	ϑ̃	ϑ̃	PROPN
ejpam-6331	98	59	⌝	⌝	PROPN
ejpam-6331	98	60	)	)	PUNCT
ejpam-6331	98	61	,	,	PUNCT
ejpam-6331	98	62	φ̃c(	φ̃c(	PROPN
ejpam-6331	98	63	⌜	⌜	PROPN
ejpam-6331	98	64	ϑ̃	ϑ̃	PROPN
ejpam-6331	98	65	⌝	⌝	PROPN
ejpam-6331	98	66	)e	)e	NOUN
ejpam-6331	98	67	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	98	68	⌜	⌜	PROPN
ejpam-6331	98	69	ϑ̃	ϑ̃	PROPN
ejpam-6331	98	70	⌝	⌝	PROPN
ejpam-6331	98	71	)	)	PUNCT
ejpam-6331	98	72	}	}	PUNCT
ejpam-6331	98	73	,	,	PUNCT
ejpam-6331	98	74	for	for	ADP
ejpam-6331	98	75	all	all	DET
ejpam-6331	98	76	⌜	⌜	PROPN
ejpam-6331	98	77	ϱ̃	ϱ̃	PROPN
ejpam-6331	98	78	⌝	⌝	PROPN
ejpam-6331	98	79	,	,	PUNCT
ejpam-6331	98	80	⌜	⌜	PROPN
ejpam-6331	98	81	ϑ̃	ϑ̃	PROPN
ejpam-6331	98	82	⌝	⌝	PROPN
ejpam-6331	98	83	∈	∈	PROPN
ejpam-6331	98	84	x	x	X
ejpam-6331	98	85	.	.	PUNCT
ejpam-6331	99	1	hence	hence	ADV
ejpam-6331	99	2	,	,	PUNCT
ejpam-6331	99	3	a	a	DET
ejpam-6331	99	4	=	=	X
ejpam-6331	99	5	(	(	PUNCT
ejpam-6331	99	6	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	99	7	,	,	PUNCT
ejpam-6331	99	8	φ̃ce	φ̃ce	PROPN
ejpam-6331	99	9	iθ̃c	iθ̃c	PROPN
ejpam-6331	99	10	)	)	PUNCT
ejpam-6331	99	11	is	be	AUX
ejpam-6331	99	12	a	a	DET
ejpam-6331	99	13	cif	cif	PROPN
ejpam-6331	99	14	-	-	PUNCT
ejpam-6331	99	15	ideal	ideal	NOUN
ejpam-6331	99	16	of	of	ADP
ejpam-6331	99	17	x	x	PROPN
ejpam-6331	99	18	.	.	PUNCT
ejpam-6331	99	19	remark	remark	PROPN
ejpam-6331	99	20	1	1	NUM
ejpam-6331	99	21	.	.	PUNCT
ejpam-6331	100	1	the	the	DET
ejpam-6331	100	2	converse	converse	NOUN
ejpam-6331	100	3	of	of	ADP
ejpam-6331	100	4	theorem	theorem	ADJ
ejpam-6331	100	5	1	1	NUM
ejpam-6331	100	6	fails	fail	VERB
ejpam-6331	100	7	to	to	PART
ejpam-6331	100	8	hold	hold	VERB
ejpam-6331	100	9	in	in	ADP
ejpam-6331	100	10	general	general	ADJ
ejpam-6331	100	11	.	.	PUNCT
ejpam-6331	101	1	example	example	NOUN
ejpam-6331	102	1	3	3	X
ejpam-6331	102	2	.	.	PUNCT
ejpam-6331	102	3	let	let	VERB
ejpam-6331	102	4	x	x	PUNCT
ejpam-6331	102	5	=	=	PUNCT
ejpam-6331	102	6	{	{	PUNCT
ejpam-6331	102	7	0	0	NUM
ejpam-6331	102	8	,	,	PUNCT
ejpam-6331	102	9	τ̃	τ̃	PROPN
ejpam-6331	102	10	,	,	PUNCT
ejpam-6331	102	11	υ̃	υ̃	PROPN
ejpam-6331	102	12	,	,	PUNCT
ejpam-6331	102	13	ζ̃	ζ̃	PROPN
ejpam-6331	102	14	,	,	PUNCT
ejpam-6331	102	15	σ̃	σ̃	PROPN
ejpam-6331	102	16	}	}	PUNCT
ejpam-6331	102	17	be	be	AUX
ejpam-6331	102	18	a	a	DET
ejpam-6331	102	19	bci	bci	NOUN
ejpam-6331	102	20	-	-	NOUN
ejpam-6331	102	21	algebra	algebra	NOUN
ejpam-6331	102	22	in	in	ADP
ejpam-6331	102	23	table	table	NOUN
ejpam-6331	102	24	3	3	NUM
ejpam-6331	102	25	.	.	PUNCT
ejpam-6331	103	1	let	let	VERB
ejpam-6331	103	2	c	c	NOUN
ejpam-6331	103	3	=	=	SYM
ejpam-6331	103	4	(	(	PUNCT
ejpam-6331	103	5	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	103	6	,	,	PUNCT
ejpam-6331	103	7	φ̃ce	φ̃ce	PROPN
ejpam-6331	103	8	iθ̃c	iθ̃c	PROPN
ejpam-6331	103	9	)	)	PUNCT
ejpam-6331	103	10	table	table	NOUN
ejpam-6331	103	11	3	3	NUM
ejpam-6331	103	12	:	:	PUNCT
ejpam-6331	103	13	(	(	PUNCT
ejpam-6331	103	14	x	x	X
ejpam-6331	103	15	,	,	PUNCT
ejpam-6331	103	16	∗	∗	NOUN
ejpam-6331	103	17	)	)	PUNCT
ejpam-6331	103	18	*	*	PUNCT
ejpam-6331	103	19	0	0	PUNCT
ejpam-6331	104	1	τ̃	τ̃	PROPN
ejpam-6331	104	2	υ̃	υ̃	PROPN
ejpam-6331	104	3	ζ̃	ζ̃	PROPN
ejpam-6331	104	4	σ̃	σ̃	PROPN
ejpam-6331	104	5	0	0	NUM
ejpam-6331	104	6	0	0	NUM
ejpam-6331	104	7	0	0	NUM
ejpam-6331	105	1	σ̃	σ̃	PROPN
ejpam-6331	105	2	ζ̃	ζ̃	PROPN
ejpam-6331	105	3	υ̃	υ̃	PROPN
ejpam-6331	105	4	τ̃	τ̃	PROPN
ejpam-6331	105	5	τ̃	τ̃	PROPN
ejpam-6331	105	6	0	0	NUM
ejpam-6331	106	1	σ̃	σ̃	PROPN
ejpam-6331	106	2	ζ̃	ζ̃	PROPN
ejpam-6331	106	3	υ̃	υ̃	PROPN
ejpam-6331	106	4	υ̃	υ̃	PROPN
ejpam-6331	106	5	υ̃	υ̃	PROPN
ejpam-6331	106	6	υ̃	υ̃	PROPN
ejpam-6331	106	7	0	0	NUM
ejpam-6331	107	1	σ̃	σ̃	PROPN
ejpam-6331	107	2	ζ̃	ζ̃	PROPN
ejpam-6331	107	3	ζ̃	ζ̃	PROPN
ejpam-6331	107	4	ζ̃	ζ̃	PROPN
ejpam-6331	107	5	ζ̃	ζ̃	PROPN
ejpam-6331	107	6	υ̃	υ̃	PROPN
ejpam-6331	107	7	0	0	PUNCT
ejpam-6331	108	1	σ̃	σ̃	PROPN
ejpam-6331	108	2	σ̃	σ̃	PROPN
ejpam-6331	108	3	σ̃	σ̃	PROPN
ejpam-6331	108	4	σ̃	σ̃	PROPN
ejpam-6331	108	5	ζ̃	ζ̃	PROPN
ejpam-6331	108	6	υ̃	υ̃	PROPN
ejpam-6331	108	7	0	0	PUNCT
ejpam-6331	108	8	be	be	AUX
ejpam-6331	108	9	a	a	DET
ejpam-6331	108	10	cif	cif	PROPN
ejpam-6331	108	11	-	-	PUNCT
ejpam-6331	108	12	set	set	NOUN
ejpam-6331	108	13	in	in	ADP
ejpam-6331	108	14	x	x	PUNCT
ejpam-6331	108	15	which	which	PRON
ejpam-6331	108	16	is	be	AUX
ejpam-6331	108	17	given	give	VERB
ejpam-6331	108	18	by	by	ADP
ejpam-6331	108	19	table	table	NOUN
ejpam-6331	108	20	4	4	NUM
ejpam-6331	108	21	.	.	PUNCT
ejpam-6331	108	22	using	use	VERB
ejpam-6331	108	23	the	the	DET
ejpam-6331	108	24	routine	routine	ADJ
ejpam-6331	108	25	calculation	calculation	NOUN
ejpam-6331	108	26	,	,	PUNCT
ejpam-6331	108	27	we	we	PRON
ejpam-6331	108	28	obtained	obtain	VERB
ejpam-6331	108	29	that	that	SCONJ
ejpam-6331	108	30	c	c	PROPN
ejpam-6331	108	31	is	be	AUX
ejpam-6331	108	32	a	a	DET
ejpam-6331	108	33	cif	cif	PROPN
ejpam-6331	108	34	-	-	PUNCT
ejpam-6331	108	35	ideal	ideal	NOUN
ejpam-6331	108	36	of	of	ADP
ejpam-6331	108	37	x	x	SYM
ejpam-6331	108	38	,	,	PUNCT
ejpam-6331	108	39	but	but	CCONJ
ejpam-6331	108	40	not	not	PART
ejpam-6331	108	41	a	a	DET
ejpam-6331	108	42	cifqa	cifqa	NOUN
ejpam-6331	108	43	-	-	PUNCT
ejpam-6331	108	44	ideal	ideal	NOUN
ejpam-6331	108	45	as	as	ADP
ejpam-6331	108	46	∅̃c(σ̃	∅̃c(σ̃	NOUN
ejpam-6331	108	47	∗	∗	NOUN
ejpam-6331	108	48	υ̃)eiω̃c(σ̃∗υ̃	υ̃)eiω̃c(σ̃∗υ̃	PUNCT
ejpam-6331	108	49	)	)	PUNCT
ejpam-6331	108	50	=	=	SYM
ejpam-6331	108	51	∅̃c(ζ̃)eiω̃c(ζ̃	∅̃c(ζ̃)eiω̃c(ζ̃	NOUN
ejpam-6331	108	52	)	)	PUNCT
ejpam-6331	108	53	t.	t.	PROPN
ejpam-6331	108	54	ramesh	ramesh	PROPN
ejpam-6331	108	55	,	,	PUNCT
ejpam-6331	108	56	m.	m.	NOUN
ejpam-6331	108	57	balamurugan	balamurugan	PROPN
ejpam-6331	108	58	,	,	PUNCT
ejpam-6331	108	59	a.	a.	NOUN
ejpam-6331	108	60	iampan	iampan	PROPN
ejpam-6331	108	61	/	/	SYM
ejpam-6331	108	62	eur	eur	PROPN
ejpam-6331	108	63	.	.	PUNCT
ejpam-6331	109	1	j.	j.	PROPN
ejpam-6331	109	2	pure	pure	PROPN
ejpam-6331	109	3	appl	appl	PROPN
ejpam-6331	109	4	.	.	PROPN
ejpam-6331	109	5	math	math	PROPN
ejpam-6331	109	6	,	,	PUNCT
ejpam-6331	109	7	18	18	NUM
ejpam-6331	109	8	(	(	PUNCT
ejpam-6331	109	9	3	3	NUM
ejpam-6331	109	10	)	)	PUNCT
ejpam-6331	109	11	(	(	PUNCT
ejpam-6331	109	12	2025	2025	NUM
ejpam-6331	109	13	)	)	PUNCT
ejpam-6331	109	14	,	,	PUNCT
ejpam-6331	109	15	6331	6331	NUM
ejpam-6331	109	16	6	6	NUM
ejpam-6331	109	17	of	of	ADP
ejpam-6331	109	18	14	14	NUM
ejpam-6331	109	19	table	table	NOUN
ejpam-6331	109	20	4	4	NUM
ejpam-6331	109	21	:	:	PUNCT
ejpam-6331	109	22	the	the	DET
ejpam-6331	109	23	values	value	NOUN
ejpam-6331	109	24	of	of	ADP
ejpam-6331	109	25	(	(	PUNCT
ejpam-6331	109	26	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	109	27	,	,	PUNCT
ejpam-6331	109	28	φ̃ce	φ̃ce	PROPN
ejpam-6331	109	29	iθ̃c	iθ̃c	PROPN
ejpam-6331	109	30	)	)	PUNCT
ejpam-6331	109	31	x	x	X
ejpam-6331	109	32	∅̃ceiω̃c	∅̃ceiω̃c	PUNCT
ejpam-6331	109	33	φ̃ce	φ̃ce	VERB
ejpam-6331	109	34	iθ̃c	iθ̃c	NOUN
ejpam-6331	109	35	0	0	NUM
ejpam-6331	109	36	0.7e	0.7e	NOUN
ejpam-6331	110	1	iπ	iπ	ADV
ejpam-6331	110	2	2	2	NUM
ejpam-6331	110	3	0.2e	0.2e	NOUN
ejpam-6331	110	4	iπ	iπ	ADV
ejpam-6331	110	5	7	7	NUM
ejpam-6331	111	1	τ̃	τ̃	NOUN
ejpam-6331	111	2	0.5e	0.5e	NUM
ejpam-6331	112	1	iπ	iπ	ADV
ejpam-6331	112	2	3	3	NUM
ejpam-6331	112	3	0.3e	0.3e	NOUN
ejpam-6331	112	4	iπ	iπ	ADV
ejpam-6331	112	5	5	5	NUM
ejpam-6331	112	6	υ̃	υ̃	PROPN
ejpam-6331	112	7	0.3e	0.3e	VERB
ejpam-6331	112	8	iπ	iπ	ADV
ejpam-6331	112	9	5	5	NUM
ejpam-6331	112	10	0.4e	0.4e	NOUN
ejpam-6331	112	11	iπ	iπ	ADV
ejpam-6331	112	12	4	4	NUM
ejpam-6331	112	13	ζ̃	ζ̃	PROPN
ejpam-6331	112	14	0.3e	0.3e	NOUN
ejpam-6331	112	15	iπ	iπ	ADV
ejpam-6331	112	16	4	4	NUM
ejpam-6331	112	17	0.4e	0.4e	NOUN
ejpam-6331	112	18	iπ	iπ	PRON
ejpam-6331	112	19	3	3	NUM
ejpam-6331	113	1	σ̃	σ̃	NOUN
ejpam-6331	113	2	0.3e	0.3e	VERB
ejpam-6331	113	3	iπ	iπ	ADV
ejpam-6331	113	4	3	3	NUM
ejpam-6331	113	5	0.4e	0.4e	NOUN
ejpam-6331	113	6	iπ	iπ	PRON
ejpam-6331	113	7	2	2	NUM
ejpam-6331	114	1	=	=	SYM
ejpam-6331	114	2	0.3e	0.3e	VERB
ejpam-6331	114	3	iπ	iπ	ADJ
ejpam-6331	114	4	4	4	NUM
ejpam-6331	114	5	≱	≱	NUM
ejpam-6331	114	6	0.7e	0.7e	VERB
ejpam-6331	114	7	iπ	iπ	ADV
ejpam-6331	114	8	2	2	NUM
ejpam-6331	114	9	=	=	SYM
ejpam-6331	114	10	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	X
ejpam-6331	114	11	)	)	PUNCT
ejpam-6331	115	1	=	=	PUNCT
ejpam-6331	115	2	min{∅̃c(σ̃	min{∅̃c(σ̃	VERB
ejpam-6331	115	3	∗	∗	NOUN
ejpam-6331	115	4	(	(	PUNCT
ejpam-6331	115	5	0	0	NUM
ejpam-6331	115	6	∗	∗	NOUN
ejpam-6331	115	7	υ̃))eiω̃c(σ̃∗(0∗υ̃	υ̃))eiω̃c(σ̃∗(0∗υ̃	NOUN
ejpam-6331	115	8	)	)	PUNCT
ejpam-6331	115	9	)	)	PUNCT
ejpam-6331	115	10	,	,	PUNCT
ejpam-6331	115	11	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	NOUN
ejpam-6331	115	12	)	)	PUNCT
ejpam-6331	115	13	}	}	PUNCT
ejpam-6331	115	14	and	and	CCONJ
ejpam-6331	115	15	φ̃c(σ̃	φ̃c(σ̃	VERB
ejpam-6331	115	16	∗	∗	NOUN
ejpam-6331	115	17	υ̃)eiθ̃c(d∗υ̃	υ̃)eiθ̃c(d∗υ̃	PROPN
ejpam-6331	115	18	)	)	PUNCT
ejpam-6331	115	19	=	=	SYM
ejpam-6331	115	20	φ̃c(ζ̃)e	φ̃c(ζ̃)e	NUM
ejpam-6331	115	21	iθ̃c(ζ̃	iθ̃c(ζ̃	NOUN
ejpam-6331	115	22	)	)	PUNCT
ejpam-6331	115	23	=	=	SYM
ejpam-6331	116	1	0.4e	0.4e	NOUN
ejpam-6331	117	1	iπ	iπ	ADV
ejpam-6331	117	2	3	3	NUM
ejpam-6331	117	3	≰	≰	NOUN
ejpam-6331	117	4	0.2e	0.2e	VERB
ejpam-6331	117	5	iπ	iπ	ADV
ejpam-6331	117	6	7	7	NUM
ejpam-6331	117	7	=	=	SYM
ejpam-6331	117	8	φ̃c(0)e	φ̃c(0)e	PRON
ejpam-6331	117	9	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	117	10	)	)	PUNCT
ejpam-6331	117	11	=	=	SYM
ejpam-6331	117	12	max{φ̃c(σ̃	max{φ̃c(σ̃	ADJ
ejpam-6331	117	13	∗	∗	NOUN
ejpam-6331	117	14	(	(	PUNCT
ejpam-6331	117	15	0	0	NUM
ejpam-6331	117	16	∗	∗	NOUN
ejpam-6331	117	17	υ̃))eiθ̃c(σ̃∗(0∗υ̃	υ̃))eiθ̃c(σ̃∗(0∗υ̃	NOUN
ejpam-6331	117	18	)	)	PUNCT
ejpam-6331	117	19	)	)	PUNCT
ejpam-6331	117	20	,	,	PUNCT
ejpam-6331	117	21	φ̃c(0)e	φ̃c(0)e	NOUN
ejpam-6331	117	22	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	117	23	)	)	PUNCT
ejpam-6331	117	24	}	}	PUNCT
ejpam-6331	117	25	.	.	PUNCT
ejpam-6331	118	1	remark	remark	NOUN
ejpam-6331	118	2	2	2	NUM
ejpam-6331	118	3	.	.	PUNCT
ejpam-6331	119	1	since	since	SCONJ
ejpam-6331	119	2	example	example	NOUN
ejpam-6331	119	3	3	3	NUM
ejpam-6331	119	4	shows	show	VERB
ejpam-6331	119	5	that	that	SCONJ
ejpam-6331	119	6	cif	cif	PROPN
ejpam-6331	119	7	-	-	PUNCT
ejpam-6331	119	8	ideals	ideal	NOUN
ejpam-6331	119	9	need	need	AUX
ejpam-6331	119	10	not	not	PART
ejpam-6331	119	11	be	be	AUX
ejpam-6331	119	12	cifqa	cifqa	NOUN
ejpam-6331	119	13	-	-	PUNCT
ejpam-6331	119	14	ideals	ideal	NOUN
ejpam-6331	119	15	,	,	PUNCT
ejpam-6331	119	16	we	we	PRON
ejpam-6331	119	17	determine	determine	VERB
ejpam-6331	119	18	the	the	DET
ejpam-6331	119	19	exact	exact	ADJ
ejpam-6331	119	20	conditions	condition	NOUN
ejpam-6331	119	21	under	under	ADP
ejpam-6331	119	22	which	which	PRON
ejpam-6331	119	23	this	this	DET
ejpam-6331	119	24	inclusion	inclusion	NOUN
ejpam-6331	119	25	holds	hold	VERB
ejpam-6331	119	26	in	in	ADP
ejpam-6331	119	27	theorem	theorem	ADJ
ejpam-6331	119	28	2	2	NUM
ejpam-6331	119	29	.	.	PUNCT
ejpam-6331	119	30	theorem	theorem	NOUN
ejpam-6331	119	31	2	2	NUM
ejpam-6331	119	32	.	.	PUNCT
ejpam-6331	120	1	if	if	SCONJ
ejpam-6331	120	2	the	the	DET
ejpam-6331	120	3	relations	relation	NOUN
ejpam-6331	120	4	(	(	PUNCT
ejpam-6331	120	5	⌜	⌜	NOUN
ejpam-6331	120	6	ϱ̃	ϱ̃	PROPN
ejpam-6331	120	7	⌝	⌝	PROPN
ejpam-6331	120	8	∗	∗	NOUN
ejpam-6331	120	9	⌜	⌜	PROPN
ejpam-6331	120	10	ϑ̃	ϑ̃	PROPN
ejpam-6331	120	11	⌝	⌝	PROPN
ejpam-6331	120	12	)	)	PUNCT
ejpam-6331	120	13	∗	∗	NOUN
ejpam-6331	120	14	⌜	⌜	PROPN
ejpam-6331	120	15	κ̃	κ̃	PROPN
ejpam-6331	120	16	⌝	⌝	PROPN
ejpam-6331	120	17	≤	≤	NOUN
ejpam-6331	120	18	⌜	⌜	PUNCT
ejpam-6331	120	19	ϱ̃	ϱ̃	PROPN
ejpam-6331	120	20	⌝	⌝	PROPN
ejpam-6331	120	21	∗	∗	NOUN
ejpam-6331	120	22	(	(	PUNCT
ejpam-6331	120	23	⌜	⌜	PROPN
ejpam-6331	120	24	ϑ̃	ϑ̃	PROPN
ejpam-6331	120	25	⌝	⌝	PROPN
ejpam-6331	120	26	∗	∗	NOUN
ejpam-6331	120	27	⌜	⌜	PROPN
ejpam-6331	120	28	κ̃	κ̃	PROPN
ejpam-6331	120	29	⌝	⌝	PROPN
ejpam-6331	120	30	)	)	PUNCT
ejpam-6331	120	31	is	be	AUX
ejpam-6331	120	32	holds	hold	NOUN
ejpam-6331	120	33	for	for	ADP
ejpam-6331	120	34	all	all	DET
ejpam-6331	120	35	⌜	⌜	PROPN
ejpam-6331	120	36	ϱ̃	ϱ̃	PROPN
ejpam-6331	120	37	⌝	⌝	PROPN
ejpam-6331	120	38	,	,	PUNCT
ejpam-6331	120	39	⌜	⌜	PROPN
ejpam-6331	120	40	ϑ̃	ϑ̃	PROPN
ejpam-6331	120	41	⌝	⌝	PROPN
ejpam-6331	120	42	,	,	PUNCT
ejpam-6331	121	1	⌜	⌜	PROPN
ejpam-6331	121	2	κ̃	κ̃	PROPN
ejpam-6331	121	3	⌝	⌝	PROPN
ejpam-6331	121	4	∈	∈	PROPN
ejpam-6331	122	1	xand	xand	NOUN
ejpam-6331	122	2	x	x	PUNCT
ejpam-6331	122	3	is	be	AUX
ejpam-6331	122	4	quasi	quasi	ADJ
ejpam-6331	122	5	-	-	NOUN
ejpam-6331	122	6	associative	associative	ADJ
ejpam-6331	122	7	in	in	ADP
ejpam-6331	122	8	bci	bci	NOUN
ejpam-6331	122	9	-	-	NOUN
ejpam-6331	122	10	algebra	algebra	NOUN
ejpam-6331	122	11	,	,	PUNCT
ejpam-6331	122	12	then	then	ADV
ejpam-6331	122	13	every	every	DET
ejpam-6331	122	14	cif	cif	PROPN
ejpam-6331	122	15	-	-	PUNCT
ejpam-6331	122	16	ideal	ideal	NOUN
ejpam-6331	122	17	is	be	AUX
ejpam-6331	122	18	a	a	DET
ejpam-6331	122	19	cifqa	cifqa	NOUN
ejpam-6331	122	20	-	-	PUNCT
ejpam-6331	122	21	ideal	ideal	NOUN
ejpam-6331	122	22	.	.	PUNCT
ejpam-6331	123	1	proof	proof	NOUN
ejpam-6331	123	2	.	.	PUNCT
ejpam-6331	124	1	let	let	VERB
ejpam-6331	124	2	a	a	DET
ejpam-6331	124	3	=	=	X
ejpam-6331	124	4	(	(	PUNCT
ejpam-6331	124	5	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	124	6	,	,	PUNCT
ejpam-6331	124	7	φ̃ce	φ̃ce	PROPN
ejpam-6331	124	8	iθ̃c	iθ̃c	PROPN
ejpam-6331	124	9	)	)	PUNCT
ejpam-6331	124	10	be	be	VERB
ejpam-6331	124	11	cif	cif	PROPN
ejpam-6331	124	12	-	-	PUNCT
ejpam-6331	124	13	ideal	ideal	NOUN
ejpam-6331	124	14	of	of	ADP
ejpam-6331	124	15	x	x	PUNCT
ejpam-6331	124	16	,	,	PUNCT
ejpam-6331	124	17	and	and	CCONJ
ejpam-6331	124	18	x	x	ADJ
ejpam-6331	124	19	be	be	AUX
ejpam-6331	124	20	the	the	DET
ejpam-6331	124	21	quasi	quasi	NOUN
ejpam-6331	124	22	-	-	NOUN
ejpam-6331	124	23	associative	associative	ADJ
ejpam-6331	124	24	(	(	PUNCT
ejpam-6331	124	25	⌜	⌜	NOUN
ejpam-6331	124	26	ϱ̃	ϱ̃	PROPN
ejpam-6331	124	27	⌝	⌝	PROPN
ejpam-6331	124	28	∗	∗	NOUN
ejpam-6331	124	29	⌜	⌜	PROPN
ejpam-6331	124	30	ϑ̃	ϑ̃	PROPN
ejpam-6331	124	31	⌝	⌝	PROPN
ejpam-6331	124	32	)	)	PUNCT
ejpam-6331	124	33	∗	∗	NOUN
ejpam-6331	124	34	⌜	⌜	PROPN
ejpam-6331	124	35	κ̃	κ̃	PROPN
ejpam-6331	124	36	⌝	⌝	PROPN
ejpam-6331	124	37	≤	≤	NOUN
ejpam-6331	124	38	⌜	⌜	PUNCT
ejpam-6331	124	39	ϱ̃	ϱ̃	PROPN
ejpam-6331	124	40	⌝	⌝	PROPN
ejpam-6331	124	41	∗	∗	NOUN
ejpam-6331	124	42	(	(	PUNCT
ejpam-6331	124	43	⌜	⌜	PROPN
ejpam-6331	124	44	ϑ̃	ϑ̃	PROPN
ejpam-6331	124	45	⌝	⌝	PROPN
ejpam-6331	124	46	∗	∗	NOUN
ejpam-6331	124	47	⌜	⌜	PROPN
ejpam-6331	124	48	κ̃	κ̃	PROPN
ejpam-6331	124	49	⌝	⌝	PROPN
ejpam-6331	124	50	)	)	PUNCT
ejpam-6331	124	51	is	be	AUX
ejpam-6331	124	52	valid	valid	ADJ
ejpam-6331	124	53	for	for	ADP
ejpam-6331	124	54	all	all	DET
ejpam-6331	124	55	⌜	⌜	PROPN
ejpam-6331	124	56	ϱ̃	ϱ̃	PROPN
ejpam-6331	124	57	⌝	⌝	PROPN
ejpam-6331	124	58	,	,	PUNCT
ejpam-6331	124	59	⌜	⌜	PROPN
ejpam-6331	124	60	ϑ̃	ϑ̃	PROPN
ejpam-6331	124	61	⌝	⌝	PROPN
ejpam-6331	124	62	,	,	PUNCT
ejpam-6331	124	63	⌜	⌜	PROPN
ejpam-6331	124	64	κ̃	κ̃	PROPN
ejpam-6331	124	65	⌝	⌝	PROPN
ejpam-6331	124	66	∈	∈	PROPN
ejpam-6331	124	67	x	x	X
ejpam-6331	124	68	.	.	PUNCT
ejpam-6331	125	1	by	by	ADP
ejpam-6331	125	2	lemma	lemma	PROPN
ejpam-6331	125	3	1	1	NUM
ejpam-6331	125	4	,	,	PUNCT
ejpam-6331	125	5	for	for	ADP
ejpam-6331	125	6	every	every	DET
ejpam-6331	125	7	cif	cif	PROPN
ejpam-6331	125	8	-	-	PUNCT
ejpam-6331	125	9	ideal	ideal	NOUN
ejpam-6331	125	10	c	c	NOUN
ejpam-6331	125	11	=	=	SYM
ejpam-6331	125	12	(	(	PUNCT
ejpam-6331	125	13	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	125	14	,	,	PUNCT
ejpam-6331	125	15	φ̃ce	φ̃ce	VERB
ejpam-6331	125	16	iθ̃c	iθ̃c	PROPN
ejpam-6331	125	17	)	)	PUNCT
ejpam-6331	125	18	.	.	PUNCT
ejpam-6331	126	1	then	then	ADV
ejpam-6331	126	2	∅̃ceiω̃c	∅̃ceiω̃c	PRON
ejpam-6331	126	3	is	be	AUX
ejpam-6331	126	4	order	order	NOUN
ejpam-6331	126	5	-	-	PUNCT
ejpam-6331	126	6	reversing	reverse	VERB
ejpam-6331	126	7	and	and	CCONJ
ejpam-6331	126	8	φ̃ce	φ̃ce	VERB
ejpam-6331	126	9	iθ̃c	iθ̃c	PROPN
ejpam-6331	126	10	is	be	AUX
ejpam-6331	126	11	order	order	NOUN
ejpam-6331	126	12	-	-	PUNCT
ejpam-6331	126	13	preserving	preserve	VERB
ejpam-6331	126	14	,	,	PUNCT
ejpam-6331	126	15	we	we	PRON
ejpam-6331	126	16	have	have	VERB
ejpam-6331	126	17	∅̃c((	∅̃c((	PROPN
ejpam-6331	126	18	⌜	⌜	NOUN
ejpam-6331	126	19	ϱ̃	ϱ̃	PROPN
ejpam-6331	126	20	⌝	⌝	PROPN
ejpam-6331	126	21	∗	∗	NOUN
ejpam-6331	126	22	⌜	⌜	PROPN
ejpam-6331	126	23	ϑ̃	ϑ̃	PROPN
ejpam-6331	126	24	⌝	⌝	PROPN
ejpam-6331	126	25	)	)	PUNCT
ejpam-6331	126	26	∗	∗	NOUN
ejpam-6331	126	27	⌜	⌜	PROPN
ejpam-6331	126	28	κ̃	κ̃	PROPN
ejpam-6331	126	29	⌝	⌝	PROPN
ejpam-6331	126	30	)eiω̃c((	)eiω̃c((	PROPN
ejpam-6331	126	31	⌜	⌜	PROPN
ejpam-6331	126	32	ϱ̃	ϱ̃	PROPN
ejpam-6331	126	33	⌝	⌝	PROPN
ejpam-6331	126	34	∗	∗	NOUN
ejpam-6331	126	35	⌜	⌜	PROPN
ejpam-6331	126	36	ϑ̃	ϑ̃	PROPN
ejpam-6331	126	37	⌝	⌝	PROPN
ejpam-6331	126	38	)∗	)∗	PROPN
ejpam-6331	126	39	⌜	⌜	PROPN
ejpam-6331	126	40	κ̃	κ̃	PROPN
ejpam-6331	126	41	⌝	⌝	PROPN
ejpam-6331	126	42	)	)	PUNCT
ejpam-6331	126	43	≥	≥	NOUN
ejpam-6331	126	44	∅a(	∅a(	NOUN
ejpam-6331	126	45	⌜	⌜	PROPN
ejpam-6331	126	46	ϱ̃	ϱ̃	PROPN
ejpam-6331	126	47	⌝	⌝	PROPN
ejpam-6331	126	48	∗	∗	NOUN
ejpam-6331	126	49	(	(	PUNCT
ejpam-6331	126	50	⌜	⌜	PROPN
ejpam-6331	126	51	ϑ̃	ϑ̃	PROPN
ejpam-6331	126	52	⌝	⌝	PROPN
ejpam-6331	126	53	∗	∗	NOUN
ejpam-6331	126	54	⌜	⌜	PROPN
ejpam-6331	126	55	κ̃	κ̃	PROPN
ejpam-6331	126	56	⌝	⌝	PROPN
ejpam-6331	126	57	))eiω̃c((	))eiω̃c((	PROPN
ejpam-6331	126	58	⌜	⌜	PROPN
ejpam-6331	126	59	ϱ̃	ϱ̃	PROPN
ejpam-6331	126	60	⌝	⌝	PROPN
ejpam-6331	126	61	∗	∗	NOUN
ejpam-6331	126	62	⌜	⌜	PROPN
ejpam-6331	126	63	ϑ̃	ϑ̃	PROPN
ejpam-6331	126	64	⌝	⌝	PROPN
ejpam-6331	126	65	)∗	)∗	PROPN
ejpam-6331	126	66	⌜	⌜	PROPN
ejpam-6331	126	67	κ̃	κ̃	PROPN
ejpam-6331	126	68	⌝	⌝	PROPN
ejpam-6331	126	69	)	)	PUNCT
ejpam-6331	126	70	φ̃c((	φ̃c((	PROPN
ejpam-6331	126	71	⌜	⌜	PROPN
ejpam-6331	126	72	ϱ̃	ϱ̃	PROPN
ejpam-6331	126	73	⌝	⌝	PROPN
ejpam-6331	126	74	∗	∗	NOUN
ejpam-6331	126	75	⌜	⌜	PROPN
ejpam-6331	126	76	ϑ̃	ϑ̃	PROPN
ejpam-6331	126	77	⌝	⌝	PROPN
ejpam-6331	126	78	)	)	PUNCT
ejpam-6331	126	79	∗	∗	NOUN
ejpam-6331	126	80	⌜	⌜	PROPN
ejpam-6331	126	81	κ̃	κ̃	PROPN
ejpam-6331	126	82	⌝	⌝	PROPN
ejpam-6331	126	83	)eiθ̃c((	)eiθ̃c((	NOUN
ejpam-6331	126	84	⌜	⌜	PROPN
ejpam-6331	126	85	ϱ̃	ϱ̃	PROPN
ejpam-6331	126	86	⌝	⌝	PROPN
ejpam-6331	126	87	∗	∗	NOUN
ejpam-6331	126	88	⌜	⌜	PROPN
ejpam-6331	126	89	ϑ̃	ϑ̃	PROPN
ejpam-6331	126	90	⌝	⌝	PROPN
ejpam-6331	126	91	)∗	)∗	PROPN
ejpam-6331	126	92	⌜	⌜	PROPN
ejpam-6331	126	93	κ̃	κ̃	PROPN
ejpam-6331	126	94	⌝	⌝	PROPN
ejpam-6331	126	95	)	)	PUNCT
ejpam-6331	126	96	≤	≤	NOUN
ejpam-6331	126	97	φ̃c((	φ̃c((	ADP
ejpam-6331	126	98	⌜	⌜	PROPN
ejpam-6331	126	99	ϱ̃	ϱ̃	PROPN
ejpam-6331	126	100	⌝	⌝	PROPN
ejpam-6331	126	101	∗	∗	NOUN
ejpam-6331	126	102	⌜	⌜	PROPN
ejpam-6331	126	103	ϑ̃	ϑ̃	PROPN
ejpam-6331	126	104	⌝	⌝	PROPN
ejpam-6331	126	105	)	)	PUNCT
ejpam-6331	126	106	∗	∗	NOUN
ejpam-6331	126	107	⌜	⌜	PROPN
ejpam-6331	126	108	κ̃	κ̃	PROPN
ejpam-6331	126	109	⌝	⌝	PROPN
ejpam-6331	126	110	)eiθ̃c((	)eiθ̃c((	NOUN
ejpam-6331	126	111	⌜	⌜	PROPN
ejpam-6331	126	112	ϱ̃	ϱ̃	PROPN
ejpam-6331	126	113	⌝	⌝	PROPN
ejpam-6331	126	114	∗	∗	NOUN
ejpam-6331	126	115	⌜	⌜	PROPN
ejpam-6331	126	116	ϑ̃	ϑ̃	PROPN
ejpam-6331	126	117	⌝	⌝	PROPN
ejpam-6331	126	118	)∗	)∗	PROPN
ejpam-6331	126	119	⌜	⌜	PROPN
ejpam-6331	126	120	κ̃	κ̃	PROPN
ejpam-6331	126	121	⌝	⌝	PROPN
ejpam-6331	126	122	)	)	PUNCT
ejpam-6331	126	123	.	.	PUNCT
ejpam-6331	127	1	by	by	ADP
ejpam-6331	127	2	cifi-2	cifi-2	NUM
ejpam-6331	127	3	and	and	CCONJ
ejpam-6331	127	4	cifi-3	cifi-3	NOUN
ejpam-6331	127	5	in	in	ADP
ejpam-6331	127	6	definition	definition	NOUN
ejpam-6331	127	7	6	6	NUM
ejpam-6331	127	8	,	,	PUNCT
ejpam-6331	127	9	we	we	PRON
ejpam-6331	127	10	have	have	VERB
ejpam-6331	127	11	∅̃c(	∅̃c(	NOUN
ejpam-6331	127	12	⌜	⌜	NOUN
ejpam-6331	127	13	ϱ̃	ϱ̃	PROPN
ejpam-6331	127	14	⌝	⌝	PROPN
ejpam-6331	127	15	∗	∗	NOUN
ejpam-6331	127	16	⌜	⌜	PROPN
ejpam-6331	127	17	κ̃	κ̃	PROPN
ejpam-6331	127	18	⌝	⌝	PROPN
ejpam-6331	127	19	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	127	20	⌜	⌜	PROPN
ejpam-6331	127	21	ϱ̃	ϱ̃	PROPN
ejpam-6331	127	22	⌝	⌝	PROPN
ejpam-6331	127	23	∗	∗	NOUN
ejpam-6331	127	24	⌜	⌜	PROPN
ejpam-6331	127	25	κ̃	κ̃	PROPN
ejpam-6331	127	26	⌝	⌝	PROPN
ejpam-6331	127	27	)	)	PUNCT
ejpam-6331	127	28	≥	≥	NOUN
ejpam-6331	127	29	min{∅̃c((	min{∅̃c((	PROPN
ejpam-6331	127	30	⌜	⌜	PROPN
ejpam-6331	127	31	ϱ̃	ϱ̃	PROPN
ejpam-6331	127	32	⌝	⌝	PROPN
ejpam-6331	127	33	∗	∗	NOUN
ejpam-6331	127	34	⌜	⌜	PROPN
ejpam-6331	127	35	κ̃	κ̃	PROPN
ejpam-6331	127	36	⌝	⌝	PROPN
ejpam-6331	127	37	)	)	PUNCT
ejpam-6331	127	38	∗	∗	NOUN
ejpam-6331	127	39	⌜	⌜	PROPN
ejpam-6331	127	40	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	41	⌝	⌝	PROPN
ejpam-6331	127	42	)eiω̃c((	)eiω̃c((	PROPN
ejpam-6331	127	43	⌜	⌜	PROPN
ejpam-6331	127	44	ϱ̃	ϱ̃	PROPN
ejpam-6331	127	45	⌝	⌝	PROPN
ejpam-6331	127	46	∗	∗	NOUN
ejpam-6331	127	47	⌜	⌜	PROPN
ejpam-6331	127	48	κ̃	κ̃	PROPN
ejpam-6331	127	49	⌝	⌝	PROPN
ejpam-6331	127	50	)∗	)∗	PROPN
ejpam-6331	127	51	⌜	⌜	PROPN
ejpam-6331	127	52	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	53	⌝	⌝	PROPN
ejpam-6331	127	54	)	)	PUNCT
ejpam-6331	127	55	,	,	PUNCT
ejpam-6331	127	56	∅̃c(	∅̃c(	NOUN
ejpam-6331	127	57	⌜	⌜	SYM
ejpam-6331	127	58	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	59	⌝	⌝	PROPN
ejpam-6331	127	60	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	127	61	⌜	⌜	PROPN
ejpam-6331	127	62	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	63	⌝	⌝	PROPN
ejpam-6331	127	64	)	)	PUNCT
ejpam-6331	127	65	}	}	PUNCT
ejpam-6331	127	66	≥	≥	PROPN
ejpam-6331	127	67	min{∅̃c((	min{∅̃c((	PROPN
ejpam-6331	127	68	⌜	⌜	PROPN
ejpam-6331	127	69	ϱ̃	ϱ̃	PROPN
ejpam-6331	127	70	⌝	⌝	PROPN
ejpam-6331	127	71	∗	∗	NOUN
ejpam-6331	127	72	⌜	⌜	PROPN
ejpam-6331	127	73	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	74	⌝	⌝	PROPN
ejpam-6331	127	75	)	)	PUNCT
ejpam-6331	127	76	∗	∗	NOUN
ejpam-6331	127	77	⌜	⌜	PROPN
ejpam-6331	127	78	κ̃	κ̃	PROPN
ejpam-6331	127	79	⌝	⌝	PROPN
ejpam-6331	127	80	)eiω̃c((	)eiω̃c((	PROPN
ejpam-6331	127	81	⌜	⌜	PROPN
ejpam-6331	127	82	ϱ̃	ϱ̃	PROPN
ejpam-6331	127	83	⌝	⌝	PROPN
ejpam-6331	127	84	∗	∗	NOUN
ejpam-6331	127	85	⌜	⌜	PROPN
ejpam-6331	127	86	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	87	⌝	⌝	PROPN
ejpam-6331	127	88	)∗	)∗	PROPN
ejpam-6331	127	89	⌜	⌜	PROPN
ejpam-6331	127	90	κ̃	κ̃	PROPN
ejpam-6331	127	91	⌝	⌝	PROPN
ejpam-6331	127	92	)	)	PUNCT
ejpam-6331	127	93	,	,	PUNCT
ejpam-6331	127	94	∅̃c(	∅̃c(	NOUN
ejpam-6331	127	95	⌜	⌜	SYM
ejpam-6331	127	96	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	97	⌝	⌝	PROPN
ejpam-6331	127	98	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	127	99	⌜	⌜	PROPN
ejpam-6331	127	100	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	101	⌝	⌝	PROPN
ejpam-6331	127	102	)	)	PUNCT
ejpam-6331	127	103	}	}	PUNCT
ejpam-6331	127	104	≥	≥	VERB
ejpam-6331	127	105	min{∅̃c(	min{∅̃c(	PRON
ejpam-6331	127	106	⌜	⌜	PROPN
ejpam-6331	127	107	ϱ̃	ϱ̃	PROPN
ejpam-6331	127	108	⌝	⌝	PROPN
ejpam-6331	127	109	∗	∗	NOUN
ejpam-6331	127	110	(	(	PUNCT
ejpam-6331	127	111	⌜	⌜	PROPN
ejpam-6331	127	112	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	113	⌝	⌝	PROPN
ejpam-6331	127	114	∗	∗	NOUN
ejpam-6331	127	115	⌜	⌜	PROPN
ejpam-6331	127	116	κ̃	κ̃	PROPN
ejpam-6331	127	117	⌝	⌝	PROPN
ejpam-6331	127	118	))eiω̃c(	))eiω̃c(	PROPN
ejpam-6331	127	119	⌜	⌜	PROPN
ejpam-6331	127	120	ϱ̃	ϱ̃	PROPN
ejpam-6331	127	121	⌝	⌝	PROPN
ejpam-6331	127	122	∗(	∗(	NOUN
ejpam-6331	127	123	⌜	⌜	PROPN
ejpam-6331	127	124	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	125	⌝	⌝	PROPN
ejpam-6331	127	126	∗	∗	NOUN
ejpam-6331	127	127	⌜	⌜	PROPN
ejpam-6331	127	128	κ̃	κ̃	PROPN
ejpam-6331	127	129	⌝	⌝	PROPN
ejpam-6331	127	130	)	)	PUNCT
ejpam-6331	127	131	)	)	PUNCT
ejpam-6331	127	132	,	,	PUNCT
ejpam-6331	127	133	∅̃c(	∅̃c(	NOUN
ejpam-6331	127	134	⌜	⌜	SYM
ejpam-6331	127	135	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	136	⌝	⌝	PROPN
ejpam-6331	127	137	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	127	138	⌜	⌜	PROPN
ejpam-6331	127	139	ϑ̃	ϑ̃	PROPN
ejpam-6331	127	140	⌝	⌝	PROPN
ejpam-6331	127	141	)	)	PUNCT
ejpam-6331	127	142	}	}	PUNCT
ejpam-6331	127	143	t.	t.	PROPN
ejpam-6331	127	144	ramesh	ramesh	PROPN
ejpam-6331	127	145	,	,	PUNCT
ejpam-6331	127	146	m.	m.	NOUN
ejpam-6331	127	147	balamurugan	balamurugan	PROPN
ejpam-6331	127	148	,	,	PUNCT
ejpam-6331	127	149	a.	a.	NOUN
ejpam-6331	127	150	iampan	iampan	PROPN
ejpam-6331	127	151	/	/	SYM
ejpam-6331	127	152	eur	eur	PROPN
ejpam-6331	127	153	.	.	PUNCT
ejpam-6331	128	1	j.	j.	PROPN
ejpam-6331	128	2	pure	pure	PROPN
ejpam-6331	128	3	appl	appl	PROPN
ejpam-6331	128	4	.	.	PROPN
ejpam-6331	128	5	math	math	PROPN
ejpam-6331	128	6	,	,	PUNCT
ejpam-6331	128	7	18	18	NUM
ejpam-6331	128	8	(	(	PUNCT
ejpam-6331	128	9	3	3	NUM
ejpam-6331	128	10	)	)	PUNCT
ejpam-6331	128	11	(	(	PUNCT
ejpam-6331	128	12	2025	2025	NUM
ejpam-6331	128	13	)	)	PUNCT
ejpam-6331	128	14	,	,	PUNCT
ejpam-6331	128	15	6331	6331	NUM
ejpam-6331	128	16	7	7	NUM
ejpam-6331	128	17	of	of	ADP
ejpam-6331	128	18	14	14	NUM
ejpam-6331	128	19	and	and	CCONJ
ejpam-6331	128	20	φ̃c(	φ̃c(	VERB
ejpam-6331	128	21	⌜	⌜	NOUN
ejpam-6331	128	22	ϱ̃	ϱ̃	PROPN
ejpam-6331	128	23	⌝	⌝	PROPN
ejpam-6331	128	24	∗	∗	NOUN
ejpam-6331	128	25	⌜	⌜	PROPN
ejpam-6331	128	26	κ̃	κ̃	PROPN
ejpam-6331	128	27	⌝	⌝	PROPN
ejpam-6331	128	28	)eiθ̃c(	)eiθ̃c(	ADJ
ejpam-6331	128	29	⌜	⌜	PROPN
ejpam-6331	128	30	ϱ̃	ϱ̃	PROPN
ejpam-6331	128	31	⌝	⌝	PROPN
ejpam-6331	128	32	∗	∗	NOUN
ejpam-6331	128	33	⌜	⌜	PROPN
ejpam-6331	128	34	κ̃	κ̃	PROPN
ejpam-6331	128	35	⌝	⌝	PROPN
ejpam-6331	128	36	)	)	PUNCT
ejpam-6331	128	37	≤	≤	PUNCT
ejpam-6331	128	38	max{φ̃c((	max{φ̃c((	PROPN
ejpam-6331	128	39	⌜	⌜	PROPN
ejpam-6331	128	40	ϱ̃	ϱ̃	PROPN
ejpam-6331	128	41	⌝	⌝	PROPN
ejpam-6331	128	42	∗	∗	NOUN
ejpam-6331	128	43	⌜	⌜	PROPN
ejpam-6331	128	44	κ̃	κ̃	PROPN
ejpam-6331	128	45	⌝	⌝	PROPN
ejpam-6331	128	46	)	)	PUNCT
ejpam-6331	128	47	∗	∗	NOUN
ejpam-6331	128	48	⌜	⌜	PROPN
ejpam-6331	128	49	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	50	⌝	⌝	PROPN
ejpam-6331	128	51	)eiθ̃c((	)eiθ̃c((	PROPN
ejpam-6331	128	52	⌜	⌜	PROPN
ejpam-6331	128	53	ϱ̃	ϱ̃	PROPN
ejpam-6331	128	54	⌝	⌝	PROPN
ejpam-6331	128	55	∗	∗	NOUN
ejpam-6331	128	56	⌜	⌜	PROPN
ejpam-6331	128	57	κ̃	κ̃	PROPN
ejpam-6331	128	58	⌝	⌝	PROPN
ejpam-6331	128	59	)∗	)∗	PROPN
ejpam-6331	128	60	⌜	⌜	PROPN
ejpam-6331	128	61	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	62	⌝	⌝	PROPN
ejpam-6331	128	63	)	)	PUNCT
ejpam-6331	128	64	,	,	PUNCT
ejpam-6331	128	65	φ̃c(	φ̃c(	PROPN
ejpam-6331	128	66	⌜	⌜	PROPN
ejpam-6331	128	67	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	68	⌝	⌝	PROPN
ejpam-6331	128	69	)e	)e	NOUN
ejpam-6331	128	70	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	128	71	⌜	⌜	PROPN
ejpam-6331	128	72	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	73	⌝	⌝	PROPN
ejpam-6331	128	74	)	)	PUNCT
ejpam-6331	128	75	}	}	PUNCT
ejpam-6331	128	76	≤	≤	NUM
ejpam-6331	128	77	max{φ̃c((	max{φ̃c((	PROPN
ejpam-6331	128	78	⌜	⌜	PROPN
ejpam-6331	128	79	ϱ̃	ϱ̃	PROPN
ejpam-6331	128	80	⌝	⌝	PROPN
ejpam-6331	128	81	∗	∗	NOUN
ejpam-6331	128	82	⌜	⌜	PROPN
ejpam-6331	128	83	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	84	⌝	⌝	PROPN
ejpam-6331	128	85	)	)	PUNCT
ejpam-6331	128	86	∗	∗	NOUN
ejpam-6331	128	87	⌜	⌜	PROPN
ejpam-6331	128	88	κ̃	κ̃	PROPN
ejpam-6331	128	89	⌝	⌝	PROPN
ejpam-6331	128	90	)eiθ̃c((	)eiθ̃c((	NOUN
ejpam-6331	128	91	⌜	⌜	PROPN
ejpam-6331	128	92	ϱ̃	ϱ̃	PROPN
ejpam-6331	128	93	⌝	⌝	PROPN
ejpam-6331	128	94	∗	∗	NOUN
ejpam-6331	128	95	⌜	⌜	PROPN
ejpam-6331	128	96	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	97	⌝	⌝	PROPN
ejpam-6331	128	98	)∗	)∗	PROPN
ejpam-6331	128	99	⌜	⌜	PROPN
ejpam-6331	128	100	κ̃	κ̃	PROPN
ejpam-6331	128	101	⌝	⌝	PROPN
ejpam-6331	128	102	)	)	PUNCT
ejpam-6331	128	103	,	,	PUNCT
ejpam-6331	128	104	φ̃c(	φ̃c(	PROPN
ejpam-6331	128	105	⌜	⌜	PROPN
ejpam-6331	128	106	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	107	⌝	⌝	PROPN
ejpam-6331	128	108	)e	)e	NOUN
ejpam-6331	128	109	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	128	110	⌜	⌜	PROPN
ejpam-6331	128	111	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	112	⌝	⌝	PROPN
ejpam-6331	128	113	)	)	PUNCT
ejpam-6331	128	114	}	}	PUNCT
ejpam-6331	128	115	≤	≤	NUM
ejpam-6331	128	116	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	128	117	⌜	⌜	NOUN
ejpam-6331	128	118	ϱ̃	ϱ̃	PROPN
ejpam-6331	128	119	⌝	⌝	PROPN
ejpam-6331	128	120	∗	∗	NOUN
ejpam-6331	128	121	(	(	PUNCT
ejpam-6331	128	122	⌜	⌜	PROPN
ejpam-6331	128	123	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	124	⌝	⌝	PROPN
ejpam-6331	128	125	∗	∗	NOUN
ejpam-6331	128	126	⌜	⌜	PROPN
ejpam-6331	128	127	κ̃	κ̃	PROPN
ejpam-6331	128	128	⌝	⌝	PROPN
ejpam-6331	128	129	))eiθ̃c(	))eiθ̃c(	DET
ejpam-6331	128	130	⌜	⌜	PROPN
ejpam-6331	128	131	ϱ̃	ϱ̃	PROPN
ejpam-6331	128	132	⌝	⌝	PROPN
ejpam-6331	128	133	∗(	∗(	NOUN
ejpam-6331	128	134	⌜	⌜	PROPN
ejpam-6331	128	135	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	136	⌝	⌝	PROPN
ejpam-6331	128	137	∗	∗	NOUN
ejpam-6331	128	138	⌜	⌜	PROPN
ejpam-6331	128	139	κ̃	κ̃	PROPN
ejpam-6331	128	140	⌝	⌝	PROPN
ejpam-6331	128	141	)	)	PUNCT
ejpam-6331	128	142	)	)	PUNCT
ejpam-6331	128	143	,	,	PUNCT
ejpam-6331	128	144	φ̃c(	φ̃c(	PROPN
ejpam-6331	128	145	⌜	⌜	PROPN
ejpam-6331	128	146	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	147	⌝	⌝	PROPN
ejpam-6331	128	148	)e	)e	NOUN
ejpam-6331	128	149	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	128	150	⌜	⌜	PROPN
ejpam-6331	128	151	ϑ̃	ϑ̃	PROPN
ejpam-6331	128	152	⌝	⌝	PROPN
ejpam-6331	128	153	)	)	PUNCT
ejpam-6331	128	154	}	}	PUNCT
ejpam-6331	128	155	.	.	PUNCT
ejpam-6331	129	1	hence	hence	ADV
ejpam-6331	129	2	,	,	PUNCT
ejpam-6331	129	3	c	c	X
ejpam-6331	129	4	=	=	SYM
ejpam-6331	129	5	(	(	PUNCT
ejpam-6331	129	6	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	129	7	,	,	PUNCT
ejpam-6331	129	8	φ̃ce	φ̃ce	PROPN
ejpam-6331	129	9	iθ̃c	iθ̃c	PROPN
ejpam-6331	129	10	)	)	PUNCT
ejpam-6331	129	11	is	be	AUX
ejpam-6331	129	12	a	a	DET
ejpam-6331	129	13	cifqa	cifqa	NOUN
ejpam-6331	129	14	-	-	PUNCT
ejpam-6331	129	15	ideal	ideal	NOUN
ejpam-6331	129	16	of	of	ADP
ejpam-6331	129	17	x	x	X
ejpam-6331	129	18	.	.	PUNCT
ejpam-6331	130	1	corollary	corollary	ADJ
ejpam-6331	130	2	1	1	NUM
ejpam-6331	130	3	.	.	PUNCT
ejpam-6331	131	1	a	a	DET
ejpam-6331	131	2	bci	bci	NOUN
ejpam-6331	131	3	-	-	NOUN
ejpam-6331	131	4	algebra	algebra	NOUN
ejpam-6331	131	5	x	x	PUNCT
ejpam-6331	131	6	has	have	VERB
ejpam-6331	131	7	the	the	DET
ejpam-6331	131	8	property	property	NOUN
ejpam-6331	131	9	that	that	PRON
ejpam-6331	131	10	all	all	DET
ejpam-6331	131	11	cif	cif	PROPN
ejpam-6331	131	12	-	-	PUNCT
ejpam-6331	131	13	ideals	ideal	NOUN
ejpam-6331	131	14	are	be	AUX
ejpam-6331	131	15	cifqa	cifqa	NOUN
ejpam-6331	131	16	-	-	PUNCT
ejpam-6331	131	17	ideals	ideal	NOUN
ejpam-6331	131	18	if	if	SCONJ
ejpam-6331	131	19	and	and	CCONJ
ejpam-6331	131	20	only	only	ADV
ejpam-6331	131	21	if	if	SCONJ
ejpam-6331	131	22	it	it	PRON
ejpam-6331	131	23	satisfies	satisfy	VERB
ejpam-6331	131	24	0	0	NUM
ejpam-6331	131	25	∗	∗	NOUN
ejpam-6331	131	26	(	(	PUNCT
ejpam-6331	131	27	0	0	NUM
ejpam-6331	131	28	∗	∗	NOUN
ejpam-6331	131	29	⌜	⌜	PROPN
ejpam-6331	131	30	ϱ̃	ϱ̃	PROPN
ejpam-6331	131	31	⌝	⌝	PROPN
ejpam-6331	131	32	)	)	PUNCT
ejpam-6331	131	33	=	=	SYM
ejpam-6331	132	1	0	0	NUM
ejpam-6331	132	2	∗	∗	NOUN
ejpam-6331	132	3	⌜	⌜	PROPN
ejpam-6331	132	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	132	5	⌝	⌝	PROPN
ejpam-6331	132	6	.	.	PUNCT
ejpam-6331	133	1	proof	proof	NOUN
ejpam-6331	133	2	.	.	PUNCT
ejpam-6331	134	1	straightforward	straightforward	ADJ
ejpam-6331	134	2	.	.	PUNCT
ejpam-6331	135	1	proposition	proposition	NOUN
ejpam-6331	135	2	1	1	NUM
ejpam-6331	135	3	.	.	PUNCT
ejpam-6331	136	1	if	if	SCONJ
ejpam-6331	136	2	c	c	NOUN
ejpam-6331	136	3	=	=	SYM
ejpam-6331	136	4	(	(	PUNCT
ejpam-6331	136	5	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	136	6	,	,	PUNCT
ejpam-6331	136	7	φ̃ce	φ̃ce	PROPN
ejpam-6331	136	8	iθ̃c	iθ̃c	PROPN
ejpam-6331	136	9	)	)	PUNCT
ejpam-6331	136	10	is	be	AUX
ejpam-6331	136	11	a	a	DET
ejpam-6331	136	12	cifqa	cifqa	NOUN
ejpam-6331	136	13	-	-	PUNCT
ejpam-6331	136	14	ideal	ideal	NOUN
ejpam-6331	136	15	of	of	ADP
ejpam-6331	136	16	x	x	SYM
ejpam-6331	136	17	,	,	PUNCT
ejpam-6331	136	18	then	then	ADV
ejpam-6331	136	19	the	the	DET
ejpam-6331	136	20	following	follow	VERB
ejpam-6331	136	21	hold	hold	NOUN
ejpam-6331	136	22	:	:	PUNCT
ejpam-6331	136	23	(	(	PUNCT
ejpam-6331	136	24	1	1	X
ejpam-6331	136	25	)	)	PUNCT
ejpam-6331	136	26	⌜	⌜	NOUN
ejpam-6331	136	27	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	28	⌝	⌝	PROPN
ejpam-6331	136	29	≤	≤	NOUN
ejpam-6331	136	30	⌜	⌜	PROPN
ejpam-6331	136	31	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	32	⌝	⌝	PROPN
ejpam-6331	136	33	⇒	⇒	NOUN
ejpam-6331	136	34	φ̃c(	φ̃c(	VERB
ejpam-6331	136	35	⌜	⌜	NOUN
ejpam-6331	136	36	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	37	⌝	⌝	PROPN
ejpam-6331	136	38	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	136	39	⌜	⌜	PROPN
ejpam-6331	136	40	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	41	⌝	⌝	PROPN
ejpam-6331	136	42	)	)	PUNCT
ejpam-6331	136	43	≥	≥	NOUN
ejpam-6331	136	44	∅̃c(	∅̃c(	NOUN
ejpam-6331	136	45	⌜	⌜	SYM
ejpam-6331	136	46	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	47	⌝	⌝	PROPN
ejpam-6331	136	48	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	136	49	⌜	⌜	PROPN
ejpam-6331	136	50	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	51	⌝	⌝	PROPN
ejpam-6331	136	52	)	)	PUNCT
ejpam-6331	136	53	,	,	PUNCT
ejpam-6331	136	54	φ̃c(	φ̃c(	VERB
ejpam-6331	136	55	⌜	⌜	NOUN
ejpam-6331	136	56	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	57	⌝	⌝	PROPN
ejpam-6331	136	58	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	136	59	⌜	⌜	PROPN
ejpam-6331	136	60	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	61	⌝	⌝	PROPN
ejpam-6331	136	62	)	)	PUNCT
ejpam-6331	136	63	≤	≤	NOUN
ejpam-6331	136	64	φ̃c(	φ̃c(	PROPN
ejpam-6331	136	65	⌜	⌜	PROPN
ejpam-6331	136	66	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	67	⌝	⌝	PROPN
ejpam-6331	136	68	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	136	69	⌜	⌜	PROPN
ejpam-6331	136	70	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	71	⌝	⌝	PROPN
ejpam-6331	136	72	)	)	PUNCT
ejpam-6331	136	73	,	,	PUNCT
ejpam-6331	136	74	(	(	PUNCT
ejpam-6331	136	75	2	2	X
ejpam-6331	136	76	)	)	PUNCT
ejpam-6331	136	77	∅̃c(	∅̃c(	NOUN
ejpam-6331	136	78	⌜	⌜	NOUN
ejpam-6331	136	79	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	80	⌝	⌝	PROPN
ejpam-6331	136	81	∗	∗	NOUN
ejpam-6331	136	82	⌜	⌜	PROPN
ejpam-6331	136	83	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	84	⌝	⌝	PROPN
ejpam-6331	136	85	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	136	86	⌜	⌜	PROPN
ejpam-6331	136	87	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	88	⌝	⌝	PROPN
ejpam-6331	136	89	∗	∗	NOUN
ejpam-6331	136	90	⌜	⌜	PROPN
ejpam-6331	136	91	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	92	⌝	⌝	PROPN
ejpam-6331	136	93	)	)	PUNCT
ejpam-6331	136	94	=	=	SYM
ejpam-6331	136	95	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	X
ejpam-6331	136	96	)	)	PUNCT
ejpam-6331	136	97	⇒	⇒	PROPN
ejpam-6331	136	98	∅̃c(	∅̃c(	NOUN
ejpam-6331	136	99	⌜	⌜	PROPN
ejpam-6331	136	100	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	101	⌝	⌝	PROPN
ejpam-6331	136	102	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	136	103	⌜	⌜	PROPN
ejpam-6331	136	104	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	105	⌝	⌝	PROPN
ejpam-6331	136	106	)	)	PUNCT
ejpam-6331	136	107	≥	≥	NOUN
ejpam-6331	136	108	∅̃c(	∅̃c(	NOUN
ejpam-6331	136	109	⌜	⌜	SYM
ejpam-6331	136	110	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	111	⌝	⌝	PROPN
ejpam-6331	136	112	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	136	113	⌜	⌜	PROPN
ejpam-6331	136	114	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	115	⌝	⌝	PROPN
ejpam-6331	136	116	)	)	PUNCT
ejpam-6331	136	117	,	,	PUNCT
ejpam-6331	136	118	φ̃c(	φ̃c(	VERB
ejpam-6331	136	119	⌜	⌜	NOUN
ejpam-6331	136	120	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	121	⌝	⌝	PROPN
ejpam-6331	136	122	∗	∗	NOUN
ejpam-6331	136	123	⌜	⌜	PROPN
ejpam-6331	136	124	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	125	⌝	⌝	PROPN
ejpam-6331	136	126	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	136	127	⌜	⌜	PROPN
ejpam-6331	136	128	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	129	⌝	⌝	PROPN
ejpam-6331	136	130	∗	∗	NOUN
ejpam-6331	136	131	⌜	⌜	PROPN
ejpam-6331	136	132	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	133	⌝	⌝	PROPN
ejpam-6331	136	134	)	)	PUNCT
ejpam-6331	136	135	=	=	PUNCT
ejpam-6331	136	136	φ̃c(0)e	φ̃c(0)e	PRON
ejpam-6331	136	137	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	136	138	)	)	PUNCT
ejpam-6331	136	139	⇒	⇒	NOUN
ejpam-6331	136	140	φ̃c(	φ̃c(	VERB
ejpam-6331	136	141	⌜	⌜	PROPN
ejpam-6331	136	142	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	143	⌝	⌝	PROPN
ejpam-6331	136	144	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	136	145	⌜	⌜	PROPN
ejpam-6331	136	146	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	147	⌝	⌝	PROPN
ejpam-6331	136	148	)	)	PUNCT
ejpam-6331	136	149	≤	≤	NOUN
ejpam-6331	136	150	φ̃c(	φ̃c(	PROPN
ejpam-6331	136	151	⌜	⌜	PROPN
ejpam-6331	136	152	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	153	⌝	⌝	PROPN
ejpam-6331	136	154	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	136	155	⌜	⌜	PROPN
ejpam-6331	136	156	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	157	⌝	⌝	PROPN
ejpam-6331	136	158	)	)	PUNCT
ejpam-6331	136	159	,	,	PUNCT
ejpam-6331	136	160	(	(	PUNCT
ejpam-6331	136	161	3	3	X
ejpam-6331	136	162	)	)	PUNCT
ejpam-6331	136	163	∅̃c(	∅̃c(	NOUN
ejpam-6331	136	164	⌜	⌜	NOUN
ejpam-6331	136	165	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	166	⌝	⌝	PROPN
ejpam-6331	136	167	∗	∗	NOUN
ejpam-6331	136	168	⌜	⌜	PROPN
ejpam-6331	136	169	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	170	⌝	⌝	PROPN
ejpam-6331	136	171	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	136	172	⌜	⌜	PROPN
ejpam-6331	136	173	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	174	⌝	⌝	PROPN
ejpam-6331	136	175	∗	∗	NOUN
ejpam-6331	136	176	⌜	⌜	PROPN
ejpam-6331	136	177	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	178	⌝	⌝	PROPN
ejpam-6331	136	179	)	)	PUNCT
ejpam-6331	136	180	≥	≥	NOUN
ejpam-6331	136	181	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	136	182	⌜	⌜	PROPN
ejpam-6331	136	183	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	184	⌝	⌝	PROPN
ejpam-6331	136	185	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	136	186	⌜	⌜	PROPN
ejpam-6331	136	187	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	188	⌝	⌝	PROPN
ejpam-6331	136	189	)	)	PUNCT
ejpam-6331	136	190	,	,	PUNCT
ejpam-6331	136	191	∅̃c(	∅̃c(	NOUN
ejpam-6331	136	192	⌜	⌜	SYM
ejpam-6331	136	193	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	194	⌝	⌝	PROPN
ejpam-6331	136	195	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	136	196	⌜	⌜	PROPN
ejpam-6331	136	197	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	198	⌝	⌝	PROPN
ejpam-6331	136	199	)	)	PUNCT
ejpam-6331	136	200	}	}	PUNCT
ejpam-6331	136	201	,	,	PUNCT
ejpam-6331	136	202	φ̃c(	φ̃c(	VERB
ejpam-6331	136	203	⌜	⌜	NOUN
ejpam-6331	136	204	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	205	⌝	⌝	PROPN
ejpam-6331	136	206	∗	∗	NOUN
ejpam-6331	136	207	⌜	⌜	PROPN
ejpam-6331	136	208	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	209	⌝	⌝	PROPN
ejpam-6331	136	210	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	136	211	⌜	⌜	PROPN
ejpam-6331	136	212	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	213	⌝	⌝	PROPN
ejpam-6331	136	214	∗	∗	NOUN
ejpam-6331	136	215	⌜	⌜	PROPN
ejpam-6331	136	216	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	217	⌝	⌝	PROPN
ejpam-6331	136	218	)	)	PUNCT
ejpam-6331	136	219	≤	≤	NOUN
ejpam-6331	136	220	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	136	221	⌜	⌜	PROPN
ejpam-6331	136	222	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	223	⌝	⌝	PROPN
ejpam-6331	136	224	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	136	225	⌜	⌜	PROPN
ejpam-6331	136	226	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	227	⌝	⌝	PROPN
ejpam-6331	136	228	∗	∗	NOUN
ejpam-6331	136	229	⌜	⌜	PROPN
ejpam-6331	136	230	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	231	⌝	⌝	PROPN
ejpam-6331	136	232	)	)	PUNCT
ejpam-6331	136	233	,	,	PUNCT
ejpam-6331	136	234	φ̃c(	φ̃c(	PROPN
ejpam-6331	136	235	⌜	⌜	PROPN
ejpam-6331	136	236	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	237	⌝	⌝	PROPN
ejpam-6331	136	238	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	136	239	⌜	⌜	PROPN
ejpam-6331	136	240	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	241	⌝	⌝	PROPN
ejpam-6331	136	242	)	)	PUNCT
ejpam-6331	136	243	}	}	PUNCT
ejpam-6331	136	244	(	(	PUNCT
ejpam-6331	136	245	4	4	X
ejpam-6331	136	246	)	)	PUNCT
ejpam-6331	136	247	∅̃c(	∅̃c(	NOUN
ejpam-6331	136	248	⌜	⌜	NOUN
ejpam-6331	136	249	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	250	⌝	⌝	PROPN
ejpam-6331	136	251	∗	∗	NOUN
ejpam-6331	136	252	⌜	⌜	PROPN
ejpam-6331	136	253	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	254	⌝	⌝	PROPN
ejpam-6331	136	255	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	136	256	⌜	⌜	PROPN
ejpam-6331	136	257	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	258	⌝	⌝	PROPN
ejpam-6331	136	259	∗	∗	NOUN
ejpam-6331	136	260	⌜	⌜	PROPN
ejpam-6331	136	261	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	262	⌝	⌝	PROPN
ejpam-6331	136	263	)	)	PUNCT
ejpam-6331	136	264	≥	≥	NOUN
ejpam-6331	136	265	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	136	266	⌜	⌜	PROPN
ejpam-6331	136	267	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	268	⌝	⌝	PROPN
ejpam-6331	136	269	∗	∗	NOUN
ejpam-6331	136	270	⌜	⌜	PROPN
ejpam-6331	136	271	κ̃	κ̃	PROPN
ejpam-6331	136	272	⌝	⌝	PROPN
ejpam-6331	136	273	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	136	274	⌜	⌜	PROPN
ejpam-6331	136	275	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	276	⌝	⌝	PROPN
ejpam-6331	136	277	∗	∗	NOUN
ejpam-6331	136	278	⌜	⌜	PROPN
ejpam-6331	136	279	κ̃	κ̃	PROPN
ejpam-6331	136	280	⌝	⌝	PROPN
ejpam-6331	136	281	)	)	PUNCT
ejpam-6331	136	282	,	,	PUNCT
ejpam-6331	136	283	∅̃c(	∅̃c(	NOUN
ejpam-6331	136	284	⌜	⌜	SYM
ejpam-6331	136	285	κ̃	κ̃	PROPN
ejpam-6331	136	286	⌝	⌝	PROPN
ejpam-6331	136	287	∗	∗	NOUN
ejpam-6331	136	288	⌜	⌜	PROPN
ejpam-6331	136	289	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	290	⌝	⌝	PROPN
ejpam-6331	136	291	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	136	292	⌜	⌜	PROPN
ejpam-6331	136	293	κ̃	κ̃	PROPN
ejpam-6331	136	294	⌝	⌝	PROPN
ejpam-6331	136	295	∗	∗	NOUN
ejpam-6331	136	296	⌜	⌜	NOUN
ejpam-6331	136	297	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	298	⌝	⌝	PROPN
ejpam-6331	136	299	)	)	PUNCT
ejpam-6331	136	300	}	}	PUNCT
ejpam-6331	136	301	,	,	PUNCT
ejpam-6331	136	302	φ̃c(	φ̃c(	VERB
ejpam-6331	136	303	⌜	⌜	NOUN
ejpam-6331	136	304	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	305	⌝	⌝	PROPN
ejpam-6331	136	306	∗	∗	NOUN
ejpam-6331	136	307	⌜	⌜	PROPN
ejpam-6331	136	308	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	309	⌝	⌝	PROPN
ejpam-6331	136	310	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	136	311	⌜	⌜	PROPN
ejpam-6331	136	312	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	313	⌝	⌝	PROPN
ejpam-6331	136	314	∗	∗	NOUN
ejpam-6331	136	315	⌜	⌜	PROPN
ejpam-6331	136	316	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	317	⌝	⌝	PROPN
ejpam-6331	136	318	)	)	PUNCT
ejpam-6331	136	319	≤	≤	NOUN
ejpam-6331	136	320	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	136	321	⌜	⌜	PROPN
ejpam-6331	136	322	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	323	⌝	⌝	PROPN
ejpam-6331	136	324	∗	∗	NOUN
ejpam-6331	136	325	⌜	⌜	PROPN
ejpam-6331	136	326	κ̃	κ̃	PROPN
ejpam-6331	136	327	⌝	⌝	PROPN
ejpam-6331	136	328	)eiθ̃c(	)eiθ̃c(	ADJ
ejpam-6331	136	329	⌜	⌜	PROPN
ejpam-6331	136	330	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	331	⌝	⌝	PROPN
ejpam-6331	136	332	∗	∗	NOUN
ejpam-6331	136	333	⌜	⌜	PROPN
ejpam-6331	136	334	κ̃	κ̃	PROPN
ejpam-6331	136	335	⌝	⌝	PROPN
ejpam-6331	136	336	)	)	PUNCT
ejpam-6331	136	337	,	,	PUNCT
ejpam-6331	136	338	φ̃c(	φ̃c(	PROPN
ejpam-6331	136	339	⌜	⌜	PROPN
ejpam-6331	136	340	κ̃	κ̃	PROPN
ejpam-6331	136	341	⌝	⌝	PROPN
ejpam-6331	136	342	∗	∗	NOUN
ejpam-6331	136	343	⌜	⌜	PROPN
ejpam-6331	136	344	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	345	⌝	⌝	PROPN
ejpam-6331	136	346	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	136	347	⌜	⌜	PROPN
ejpam-6331	136	348	κ̃	κ̃	PROPN
ejpam-6331	136	349	⌝	⌝	PROPN
ejpam-6331	136	350	∗	∗	NOUN
ejpam-6331	136	351	⌜	⌜	NOUN
ejpam-6331	136	352	ϑ̃	ϑ̃	PROPN
ejpam-6331	136	353	⌝	⌝	PROPN
ejpam-6331	136	354	)	)	PUNCT
ejpam-6331	136	355	}	}	PUNCT
ejpam-6331	136	356	(	(	PUNCT
ejpam-6331	136	357	5	5	X
ejpam-6331	136	358	)	)	PUNCT
ejpam-6331	136	359	∅̃c((0	∅̃c((0	PROPN
ejpam-6331	136	360	∗	∗	NOUN
ejpam-6331	136	361	⌜	⌜	PROPN
ejpam-6331	136	362	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	363	⌝	⌝	PROPN
ejpam-6331	136	364	)	)	PUNCT
ejpam-6331	136	365	∗	∗	NOUN
ejpam-6331	136	366	⌜	⌜	PROPN
ejpam-6331	136	367	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	368	⌝	⌝	PROPN
ejpam-6331	136	369	)eiω̃c((0∗	)eiω̃c((0∗	PROPN
ejpam-6331	136	370	⌜	⌜	PROPN
ejpam-6331	136	371	ϱ̃	ϱ̃	PROPN
ejpam-6331	136	372	⌝	⌝	PROPN
ejpam-6331	136	373	)∗l	)∗l	PUNCT
ejpam-6331	136	374	)	)	PUNCT
ejpam-6331	137	1	=	=	SYM
ejpam-6331	137	2	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	NOUN
ejpam-6331	137	3	)	)	PUNCT
ejpam-6331	137	4	,	,	PUNCT
ejpam-6331	137	5	φ̃c((0	φ̃c((0	ADP
ejpam-6331	137	6	∗	∗	NOUN
ejpam-6331	137	7	⌜	⌜	PROPN
ejpam-6331	137	8	ϱ̃	ϱ̃	PROPN
ejpam-6331	137	9	⌝	⌝	PROPN
ejpam-6331	137	10	)	)	PUNCT
ejpam-6331	137	11	∗	∗	NOUN
ejpam-6331	137	12	⌜	⌜	PROPN
ejpam-6331	137	13	ϱ̃	ϱ̃	PROPN
ejpam-6331	137	14	⌝	⌝	PROPN
ejpam-6331	137	15	)eiθ̃c((0∗	)eiθ̃c((0∗	PROPN
ejpam-6331	137	16	⌜	⌜	PROPN
ejpam-6331	137	17	ϱ̃	ϱ̃	PROPN
ejpam-6331	137	18	⌝	⌝	PROPN
ejpam-6331	137	19	)∗	)∗	PROPN
ejpam-6331	137	20	⌜	⌜	PROPN
ejpam-6331	137	21	ϱ̃	ϱ̃	PROPN
ejpam-6331	137	22	⌝	⌝	PROPN
ejpam-6331	137	23	)	)	PUNCT
ejpam-6331	137	24	=	=	PUNCT
ejpam-6331	137	25	φ̃c(0)e	φ̃c(0)e	PRON
ejpam-6331	137	26	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	137	27	)	)	PUNCT
ejpam-6331	137	28	,	,	PUNCT
ejpam-6331	137	29	for	for	ADP
ejpam-6331	137	30	all	all	DET
ejpam-6331	137	31	⌜	⌜	PROPN
ejpam-6331	137	32	ϱ̃	ϱ̃	PROPN
ejpam-6331	137	33	⌝	⌝	PROPN
ejpam-6331	137	34	,	,	PUNCT
ejpam-6331	137	35	⌜	⌜	PROPN
ejpam-6331	137	36	ϑ̃	ϑ̃	PROPN
ejpam-6331	137	37	⌝	⌝	PROPN
ejpam-6331	137	38	,	,	PUNCT
ejpam-6331	137	39	⌜	⌜	PROPN
ejpam-6331	137	40	κ̃	κ̃	PROPN
ejpam-6331	137	41	⌝	⌝	PROPN
ejpam-6331	137	42	∈	∈	PROPN
ejpam-6331	137	43	x	x	X
ejpam-6331	137	44	.	.	PUNCT
ejpam-6331	138	1	proof	proof	NOUN
ejpam-6331	138	2	.	.	PUNCT
ejpam-6331	139	1	(	(	PUNCT
ejpam-6331	139	2	1	1	X
ejpam-6331	139	3	)	)	PUNCT
ejpam-6331	139	4	if	if	SCONJ
ejpam-6331	139	5	⌜	⌜	PROPN
ejpam-6331	139	6	ϱ̃	ϱ̃	PROPN
ejpam-6331	139	7	⌝	⌝	PROPN
ejpam-6331	139	8	≤	≤	NOUN
ejpam-6331	139	9	⌜	⌜	PROPN
ejpam-6331	139	10	ϑ̃	ϑ̃	PROPN
ejpam-6331	139	11	⌝	⌝	PROPN
ejpam-6331	139	12	,	,	PUNCT
ejpam-6331	139	13	then	then	ADV
ejpam-6331	139	14	⌜	⌜	PROPN
ejpam-6331	139	15	ϱ̃	ϱ̃	PROPN
ejpam-6331	139	16	⌝	⌝	PROPN
ejpam-6331	139	17	∗	∗	NOUN
ejpam-6331	139	18	⌜	⌜	PROPN
ejpam-6331	139	19	ϑ̃	ϑ̃	PROPN
ejpam-6331	139	20	⌝	⌝	PROPN
ejpam-6331	139	21	=	=	SYM
ejpam-6331	139	22	0	0	PROPN
ejpam-6331	139	23	.	.	PUNCT
ejpam-6331	140	1	then	then	ADV
ejpam-6331	140	2	∅̃c(	∅̃c(	NOUN
ejpam-6331	140	3	⌜	⌜	PROPN
ejpam-6331	140	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	140	5	⌝	⌝	PROPN
ejpam-6331	140	6	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	140	7	⌜	⌜	PROPN
ejpam-6331	140	8	ϱ̃	ϱ̃	PROPN
ejpam-6331	140	9	⌝	⌝	PROPN
ejpam-6331	140	10	)	)	PUNCT
ejpam-6331	140	11	=	=	SYM
ejpam-6331	140	12	∅̃c(	∅̃c(	NOUN
ejpam-6331	140	13	⌜	⌜	NOUN
ejpam-6331	141	1	ϱ̃	ϱ̃	PROPN
ejpam-6331	141	2	⌝	⌝	PROPN
ejpam-6331	141	3	∗	∗	NOUN
ejpam-6331	141	4	0)eiω̃c(	0)eiω̃c(	NUM
ejpam-6331	141	5	⌜	⌜	NOUN
ejpam-6331	141	6	ϱ̃	ϱ̃	PROPN
ejpam-6331	141	7	⌝	⌝	PROPN
ejpam-6331	141	8	∗0	∗0	PROPN
ejpam-6331	141	9	)	)	PUNCT
ejpam-6331	141	10	≥	≥	NOUN
ejpam-6331	141	11	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	141	12	⌜	⌜	PROPN
ejpam-6331	141	13	ϱ̃	ϱ̃	PROPN
ejpam-6331	141	14	⌝	⌝	PROPN
ejpam-6331	141	15	∗	∗	NOUN
ejpam-6331	141	16	(	(	PUNCT
ejpam-6331	141	17	⌜	⌜	PROPN
ejpam-6331	141	18	ϑ̃	ϑ̃	PROPN
ejpam-6331	141	19	⌝	⌝	PROPN
ejpam-6331	141	20	∗	∗	NOUN
ejpam-6331	141	21	0))eiω̃c(	0))eiω̃c(	NOUN
ejpam-6331	141	22	⌜	⌜	NOUN
ejpam-6331	141	23	ϱ̃	ϱ̃	PROPN
ejpam-6331	141	24	⌝	⌝	PROPN
ejpam-6331	141	25	∗(	∗(	NOUN
ejpam-6331	141	26	⌜	⌜	PROPN
ejpam-6331	141	27	ϑ̃	ϑ̃	PROPN
ejpam-6331	141	28	⌝	⌝	PROPN
ejpam-6331	141	29	∗0	∗0	PROPN
ejpam-6331	141	30	)	)	PUNCT
ejpam-6331	141	31	)	)	PUNCT
ejpam-6331	141	32	,	,	PUNCT
ejpam-6331	141	33	∅̃c(	∅̃c(	NOUN
ejpam-6331	141	34	⌜	⌜	SYM
ejpam-6331	141	35	ϑ̃	ϑ̃	PROPN
ejpam-6331	141	36	⌝	⌝	PROPN
ejpam-6331	141	37	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	141	38	⌜	⌜	PROPN
ejpam-6331	141	39	ϑ̃	ϑ̃	PROPN
ejpam-6331	141	40	⌝	⌝	PROPN
ejpam-6331	141	41	)	)	PUNCT
ejpam-6331	141	42	}	}	PUNCT
ejpam-6331	141	43	≥	≥	VERB
ejpam-6331	141	44	min{∅̃c(	min{∅̃c(	PRON
ejpam-6331	141	45	⌜	⌜	PROPN
ejpam-6331	142	1	ϱ̃	ϱ̃	PROPN
ejpam-6331	142	2	⌝	⌝	PROPN
ejpam-6331	142	3	∗	∗	NOUN
ejpam-6331	142	4	⌜	⌜	PROPN
ejpam-6331	142	5	ϑ̃	ϑ̃	PROPN
ejpam-6331	142	6	⌝	⌝	PROPN
ejpam-6331	142	7	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	142	8	⌜	⌜	PROPN
ejpam-6331	142	9	ϱ̃	ϱ̃	PROPN
ejpam-6331	142	10	⌝	⌝	PROPN
ejpam-6331	142	11	∗	∗	NOUN
ejpam-6331	142	12	⌜	⌜	PROPN
ejpam-6331	142	13	ϑ̃	ϑ̃	PROPN
ejpam-6331	142	14	⌝	⌝	PROPN
ejpam-6331	142	15	)	)	PUNCT
ejpam-6331	142	16	,	,	PUNCT
ejpam-6331	142	17	∅̃c(	∅̃c(	NOUN
ejpam-6331	142	18	⌜	⌜	SYM
ejpam-6331	142	19	ϑ̃	ϑ̃	PROPN
ejpam-6331	142	20	⌝	⌝	PROPN
ejpam-6331	142	21	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	142	22	⌜	⌜	PROPN
ejpam-6331	142	23	ϑ̃	ϑ̃	PROPN
ejpam-6331	142	24	⌝	⌝	PROPN
ejpam-6331	142	25	)	)	PUNCT
ejpam-6331	142	26	}	}	PUNCT
ejpam-6331	142	27	≥	≥	NOUN
ejpam-6331	142	28	min{∅̃c(0)eiω̃c(0	min{∅̃c(0)eiω̃c(0	NOUN
ejpam-6331	142	29	)	)	PUNCT
ejpam-6331	142	30	,	,	PUNCT
ejpam-6331	142	31	∅̃c(	∅̃c(	NOUN
ejpam-6331	142	32	⌜	⌜	SYM
ejpam-6331	142	33	ϑ̃	ϑ̃	PROPN
ejpam-6331	142	34	⌝	⌝	PROPN
ejpam-6331	142	35	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	142	36	⌜	⌜	PROPN
ejpam-6331	142	37	ϑ̃	ϑ̃	PROPN
ejpam-6331	142	38	⌝	⌝	PROPN
ejpam-6331	142	39	)	)	PUNCT
ejpam-6331	142	40	}	}	PUNCT
ejpam-6331	142	41	∅̃c(	∅̃c(	NOUN
ejpam-6331	142	42	⌜	⌜	PROPN
ejpam-6331	142	43	ϱ̃	ϱ̃	PROPN
ejpam-6331	142	44	⌝	⌝	PROPN
ejpam-6331	142	45	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	142	46	⌜	⌜	PROPN
ejpam-6331	142	47	ϱ̃	ϱ̃	PROPN
ejpam-6331	142	48	⌝	⌝	PROPN
ejpam-6331	142	49	)	)	PUNCT
ejpam-6331	142	50	≥	≥	NOUN
ejpam-6331	142	51	∅̃c(	∅̃c(	NOUN
ejpam-6331	142	52	⌜	⌜	SYM
ejpam-6331	142	53	ϑ̃	ϑ̃	PROPN
ejpam-6331	142	54	⌝	⌝	PROPN
ejpam-6331	142	55	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	142	56	⌜	⌜	PROPN
ejpam-6331	142	57	ϑ̃	ϑ̃	PROPN
ejpam-6331	142	58	⌝	⌝	PROPN
ejpam-6331	142	59	)	)	PUNCT
ejpam-6331	142	60	and	and	CCONJ
ejpam-6331	142	61	φ̃c(	φ̃c(	PROPN
ejpam-6331	142	62	⌜	⌜	NOUN
ejpam-6331	142	63	ϱ̃	ϱ̃	PROPN
ejpam-6331	142	64	⌝	⌝	PROPN
ejpam-6331	143	1	)e	)e	NOUN
ejpam-6331	143	2	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	143	3	⌜	⌜	PROPN
ejpam-6331	143	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	143	5	⌝	⌝	PROPN
ejpam-6331	143	6	)	)	PUNCT
ejpam-6331	144	1	=	=	PUNCT
ejpam-6331	144	2	φ̃c(	φ̃c(	PROPN
ejpam-6331	144	3	⌜	⌜	NOUN
ejpam-6331	145	1	ϱ̃	ϱ̃	PROPN
ejpam-6331	145	2	⌝	⌝	PROPN
ejpam-6331	145	3	∗	∗	NOUN
ejpam-6331	145	4	0)eiθ̃c(	0)eiθ̃c(	NUM
ejpam-6331	145	5	⌜	⌜	PROPN
ejpam-6331	145	6	ϱ̃	ϱ̃	PROPN
ejpam-6331	145	7	⌝	⌝	PROPN
ejpam-6331	145	8	∗0	∗0	PROPN
ejpam-6331	145	9	)	)	PUNCT
ejpam-6331	145	10	≤	≤	NOUN
ejpam-6331	145	11	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	145	12	⌜	⌜	PROPN
ejpam-6331	145	13	ϱ̃	ϱ̃	PROPN
ejpam-6331	145	14	⌝	⌝	PROPN
ejpam-6331	145	15	∗	∗	NOUN
ejpam-6331	145	16	(	(	PUNCT
ejpam-6331	145	17	⌜	⌜	PROPN
ejpam-6331	145	18	ϑ̃	ϑ̃	PROPN
ejpam-6331	145	19	⌝	⌝	PROPN
ejpam-6331	145	20	∗	∗	NOUN
ejpam-6331	145	21	0))eiθ̃c(	0))eiθ̃c(	PUNCT
ejpam-6331	145	22	⌜	⌜	PROPN
ejpam-6331	145	23	ϱ̃	ϱ̃	PROPN
ejpam-6331	145	24	⌝	⌝	PROPN
ejpam-6331	145	25	∗(	∗(	NOUN
ejpam-6331	145	26	⌜	⌜	PROPN
ejpam-6331	145	27	ϑ̃	ϑ̃	PROPN
ejpam-6331	145	28	⌝	⌝	PROPN
ejpam-6331	145	29	∗0	∗0	PROPN
ejpam-6331	145	30	)	)	PUNCT
ejpam-6331	145	31	)	)	PUNCT
ejpam-6331	145	32	,	,	PUNCT
ejpam-6331	145	33	φ̃c(	φ̃c(	PROPN
ejpam-6331	145	34	⌜	⌜	PROPN
ejpam-6331	145	35	ϑ̃	ϑ̃	PROPN
ejpam-6331	145	36	⌝	⌝	PROPN
ejpam-6331	145	37	)e	)e	NOUN
ejpam-6331	145	38	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	145	39	⌜	⌜	PROPN
ejpam-6331	145	40	ϑ̃	ϑ̃	PROPN
ejpam-6331	145	41	⌝	⌝	PROPN
ejpam-6331	145	42	)	)	PUNCT
ejpam-6331	145	43	}	}	PUNCT
ejpam-6331	145	44	≤	≤	NUM
ejpam-6331	145	45	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	145	46	⌜	⌜	NOUN
ejpam-6331	145	47	ϱ̃	ϱ̃	PROPN
ejpam-6331	145	48	⌝	⌝	PROPN
ejpam-6331	145	49	∗	∗	NOUN
ejpam-6331	145	50	⌜	⌜	PROPN
ejpam-6331	145	51	ϑ̃	ϑ̃	PROPN
ejpam-6331	145	52	⌝	⌝	PROPN
ejpam-6331	145	53	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	145	54	⌜	⌜	PROPN
ejpam-6331	145	55	ϱ̃	ϱ̃	PROPN
ejpam-6331	145	56	⌝	⌝	PROPN
ejpam-6331	145	57	∗	∗	NOUN
ejpam-6331	145	58	⌜	⌜	PROPN
ejpam-6331	145	59	ϑ̃	ϑ̃	PROPN
ejpam-6331	145	60	⌝	⌝	PROPN
ejpam-6331	145	61	)	)	PUNCT
ejpam-6331	145	62	,	,	PUNCT
ejpam-6331	145	63	φ̃c(	φ̃c(	PROPN
ejpam-6331	145	64	⌜	⌜	PROPN
ejpam-6331	145	65	ϑ̃	ϑ̃	PROPN
ejpam-6331	145	66	⌝	⌝	PROPN
ejpam-6331	145	67	)e	)e	NOUN
ejpam-6331	145	68	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	145	69	⌜	⌜	PROPN
ejpam-6331	145	70	ϑ̃	ϑ̃	PROPN
ejpam-6331	145	71	⌝	⌝	PROPN
ejpam-6331	145	72	)	)	PUNCT
ejpam-6331	145	73	}	}	PUNCT
ejpam-6331	145	74	t.	t.	PROPN
ejpam-6331	145	75	ramesh	ramesh	PROPN
ejpam-6331	145	76	,	,	PUNCT
ejpam-6331	145	77	m.	m.	NOUN
ejpam-6331	145	78	balamurugan	balamurugan	PROPN
ejpam-6331	145	79	,	,	PUNCT
ejpam-6331	145	80	a.	a.	NOUN
ejpam-6331	145	81	iampan	iampan	PROPN
ejpam-6331	145	82	/	/	SYM
ejpam-6331	145	83	eur	eur	PROPN
ejpam-6331	145	84	.	.	PUNCT
ejpam-6331	146	1	j.	j.	PROPN
ejpam-6331	146	2	pure	pure	PROPN
ejpam-6331	146	3	appl	appl	PROPN
ejpam-6331	146	4	.	.	PROPN
ejpam-6331	146	5	math	math	PROPN
ejpam-6331	146	6	,	,	PUNCT
ejpam-6331	146	7	18	18	NUM
ejpam-6331	146	8	(	(	PUNCT
ejpam-6331	146	9	3	3	NUM
ejpam-6331	146	10	)	)	PUNCT
ejpam-6331	146	11	(	(	PUNCT
ejpam-6331	146	12	2025	2025	NUM
ejpam-6331	146	13	)	)	PUNCT
ejpam-6331	146	14	,	,	PUNCT
ejpam-6331	146	15	6331	6331	NUM
ejpam-6331	146	16	8	8	NUM
ejpam-6331	146	17	of	of	ADP
ejpam-6331	146	18	14	14	NUM
ejpam-6331	146	19	≤	≤	NUM
ejpam-6331	146	20	max{φ̃c(0)e	max{φ̃c(0)e	NOUN
ejpam-6331	146	21	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	146	22	)	)	PUNCT
ejpam-6331	146	23	,	,	PUNCT
ejpam-6331	146	24	φ̃c(	φ̃c(	PROPN
ejpam-6331	146	25	⌜	⌜	PROPN
ejpam-6331	146	26	ϑ̃	ϑ̃	PROPN
ejpam-6331	146	27	⌝	⌝	PROPN
ejpam-6331	146	28	)e	)e	NOUN
ejpam-6331	146	29	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	146	30	⌜	⌜	PROPN
ejpam-6331	146	31	ϑ̃	ϑ̃	PROPN
ejpam-6331	146	32	⌝	⌝	PROPN
ejpam-6331	146	33	)	)	PUNCT
ejpam-6331	146	34	}	}	PUNCT
ejpam-6331	146	35	φ̃c(	φ̃c(	VERB
ejpam-6331	146	36	⌜	⌜	NOUN
ejpam-6331	146	37	ϱ̃	ϱ̃	PROPN
ejpam-6331	146	38	⌝	⌝	PROPN
ejpam-6331	146	39	)e	)e	NOUN
ejpam-6331	146	40	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	146	41	⌜	⌜	PROPN
ejpam-6331	146	42	ϱ̃	ϱ̃	PROPN
ejpam-6331	146	43	⌝	⌝	PROPN
ejpam-6331	146	44	)	)	PUNCT
ejpam-6331	146	45	≤	≤	NOUN
ejpam-6331	146	46	φ̃c(	φ̃c(	PROPN
ejpam-6331	146	47	⌜	⌜	PROPN
ejpam-6331	146	48	ϑ̃	ϑ̃	PROPN
ejpam-6331	146	49	⌝	⌝	PROPN
ejpam-6331	146	50	)e	)e	NOUN
ejpam-6331	146	51	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	146	52	⌜	⌜	PROPN
ejpam-6331	146	53	ϑ̃	ϑ̃	PROPN
ejpam-6331	146	54	⌝	⌝	PROPN
ejpam-6331	146	55	)	)	PUNCT
ejpam-6331	146	56	.	.	PUNCT
ejpam-6331	147	1	(	(	PUNCT
ejpam-6331	147	2	2	2	X
ejpam-6331	147	3	)	)	PUNCT
ejpam-6331	147	4	this	this	PRON
ejpam-6331	147	5	is	be	AUX
ejpam-6331	147	6	analogous	analogous	ADJ
ejpam-6331	147	7	to	to	ADP
ejpam-6331	147	8	(	(	PUNCT
ejpam-6331	147	9	1	1	NUM
ejpam-6331	147	10	)	)	PUNCT
ejpam-6331	147	11	.	.	PUNCT
ejpam-6331	148	1	(	(	PUNCT
ejpam-6331	148	2	3	3	X
ejpam-6331	148	3	)	)	PUNCT
ejpam-6331	148	4	let	let	VERB
ejpam-6331	148	5	⌜	⌜	PROPN
ejpam-6331	148	6	ϱ̃	ϱ̃	PROPN
ejpam-6331	148	7	⌝	⌝	PROPN
ejpam-6331	148	8	,	,	PUNCT
ejpam-6331	148	9	⌜	⌜	PROPN
ejpam-6331	148	10	ϑ̃	ϑ̃	PROPN
ejpam-6331	148	11	⌝	⌝	PROPN
ejpam-6331	148	12	∈	∈	PROPN
ejpam-6331	148	13	x	x	X
ejpam-6331	148	14	.	.	PUNCT
ejpam-6331	149	1	then	then	ADV
ejpam-6331	149	2	∅̃c(	∅̃c(	VERB
ejpam-6331	149	3	⌜	⌜	NOUN
ejpam-6331	149	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	149	5	⌝	⌝	PROPN
ejpam-6331	149	6	∗	∗	NOUN
ejpam-6331	149	7	⌜	⌜	PROPN
ejpam-6331	149	8	ϑ̃	ϑ̃	PROPN
ejpam-6331	149	9	⌝	⌝	PROPN
ejpam-6331	149	10	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	149	11	⌜	⌜	PROPN
ejpam-6331	149	12	ϱ̃	ϱ̃	PROPN
ejpam-6331	149	13	⌝	⌝	PROPN
ejpam-6331	149	14	∗	∗	NOUN
ejpam-6331	149	15	⌜	⌜	PROPN
ejpam-6331	149	16	ϑ̃	ϑ̃	PROPN
ejpam-6331	149	17	⌝	⌝	PROPN
ejpam-6331	149	18	)	)	PUNCT
ejpam-6331	149	19	≥	≥	NOUN
ejpam-6331	150	1	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	150	2	⌜	⌜	PROPN
ejpam-6331	150	3	ϱ̃	ϱ̃	PROPN
ejpam-6331	150	4	⌝	⌝	PROPN
ejpam-6331	150	5	∗	∗	NOUN
ejpam-6331	150	6	(	(	PUNCT
ejpam-6331	150	7	⌜	⌜	PROPN
ejpam-6331	150	8	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	9	⌝	⌝	PROPN
ejpam-6331	150	10	∗	∗	PROPN
ejpam-6331	150	11	⌜	⌜	PROPN
ejpam-6331	150	12	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	13	⌝	⌝	PROPN
ejpam-6331	150	14	))eiω̃c(	))eiω̃c(	PROPN
ejpam-6331	150	15	⌜	⌜	PROPN
ejpam-6331	150	16	ϱ̃	ϱ̃	PROPN
ejpam-6331	150	17	⌝	⌝	PROPN
ejpam-6331	150	18	∗(	∗(	NOUN
ejpam-6331	150	19	⌜	⌜	PROPN
ejpam-6331	150	20	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	21	⌝	⌝	PROPN
ejpam-6331	150	22	∗	∗	NOUN
ejpam-6331	150	23	⌜	⌜	PROPN
ejpam-6331	150	24	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	25	⌝	⌝	PROPN
ejpam-6331	150	26	)	)	PUNCT
ejpam-6331	150	27	)	)	PUNCT
ejpam-6331	150	28	,	,	PUNCT
ejpam-6331	150	29	∅̃c(	∅̃c(	NOUN
ejpam-6331	150	30	⌜	⌜	SYM
ejpam-6331	150	31	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	32	⌝	⌝	PROPN
ejpam-6331	150	33	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	150	34	⌜	⌜	PROPN
ejpam-6331	150	35	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	36	⌝	⌝	PROPN
ejpam-6331	150	37	)	)	PUNCT
ejpam-6331	150	38	}	}	PUNCT
ejpam-6331	150	39	≥	≥	VERB
ejpam-6331	150	40	min{∅̃c(	min{∅̃c(	PRON
ejpam-6331	150	41	⌜	⌜	PROPN
ejpam-6331	150	42	ϱ̃	ϱ̃	PROPN
ejpam-6331	150	43	⌝	⌝	PROPN
ejpam-6331	150	44	∗	∗	NOUN
ejpam-6331	150	45	0)eiω̃c(	0)eiω̃c(	NUM
ejpam-6331	150	46	⌜	⌜	NOUN
ejpam-6331	150	47	ϱ̃	ϱ̃	PROPN
ejpam-6331	150	48	⌝	⌝	PROPN
ejpam-6331	150	49	∗0	∗0	PROPN
ejpam-6331	150	50	)	)	PUNCT
ejpam-6331	150	51	,	,	PUNCT
ejpam-6331	150	52	∅̃c(	∅̃c(	NOUN
ejpam-6331	150	53	⌜	⌜	SYM
ejpam-6331	150	54	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	55	⌝	⌝	PROPN
ejpam-6331	150	56	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	150	57	⌜	⌜	PROPN
ejpam-6331	150	58	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	59	⌝	⌝	PROPN
ejpam-6331	150	60	)	)	PUNCT
ejpam-6331	150	61	}	}	PUNCT
ejpam-6331	150	62	≥	≥	VERB
ejpam-6331	150	63	min{∅̃c(	min{∅̃c(	PRON
ejpam-6331	150	64	⌜	⌜	PROPN
ejpam-6331	150	65	ϱ̃	ϱ̃	PROPN
ejpam-6331	150	66	⌝	⌝	PROPN
ejpam-6331	150	67	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	150	68	⌜	⌜	PROPN
ejpam-6331	150	69	ϱ̃	ϱ̃	PROPN
ejpam-6331	150	70	⌝	⌝	PROPN
ejpam-6331	150	71	)	)	PUNCT
ejpam-6331	150	72	,	,	PUNCT
ejpam-6331	150	73	∅̃c(	∅̃c(	NOUN
ejpam-6331	150	74	⌜	⌜	SYM
ejpam-6331	150	75	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	76	⌝	⌝	PROPN
ejpam-6331	150	77	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	150	78	⌜	⌜	PROPN
ejpam-6331	150	79	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	80	⌝	⌝	PROPN
ejpam-6331	150	81	)	)	PUNCT
ejpam-6331	150	82	}	}	PUNCT
ejpam-6331	150	83	and	and	CCONJ
ejpam-6331	150	84	φ̃c(	φ̃c(	PROPN
ejpam-6331	150	85	⌜	⌜	NOUN
ejpam-6331	150	86	ϱ̃	ϱ̃	PROPN
ejpam-6331	150	87	⌝	⌝	PROPN
ejpam-6331	150	88	∗	∗	NOUN
ejpam-6331	150	89	⌜	⌜	PROPN
ejpam-6331	150	90	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	91	⌝	⌝	PROPN
ejpam-6331	150	92	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	150	93	⌜	⌜	PROPN
ejpam-6331	150	94	ϱ̃	ϱ̃	PROPN
ejpam-6331	150	95	⌝	⌝	PROPN
ejpam-6331	150	96	∗	∗	NOUN
ejpam-6331	150	97	⌜	⌜	PROPN
ejpam-6331	150	98	ϑ̃	ϑ̃	PROPN
ejpam-6331	150	99	⌝	⌝	PROPN
ejpam-6331	150	100	)	)	PUNCT
ejpam-6331	150	101	≤	≤	NOUN
ejpam-6331	150	102	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	151	1	⌜	⌜	PROPN
ejpam-6331	151	2	ϱ̃	ϱ̃	PROPN
ejpam-6331	151	3	⌝	⌝	PROPN
ejpam-6331	151	4	∗	∗	NOUN
ejpam-6331	151	5	(	(	PUNCT
ejpam-6331	151	6	⌜	⌜	PROPN
ejpam-6331	151	7	ϑ̃	ϑ̃	PROPN
ejpam-6331	151	8	⌝	⌝	PROPN
ejpam-6331	151	9	∗	∗	PROPN
ejpam-6331	151	10	⌜	⌜	PROPN
ejpam-6331	151	11	ϑ̃	ϑ̃	PROPN
ejpam-6331	151	12	⌝	⌝	PROPN
ejpam-6331	151	13	))eiθ̃c(	))eiθ̃c(	PROPN
ejpam-6331	151	14	⌜	⌜	PROPN
ejpam-6331	151	15	ϱ̃	ϱ̃	PROPN
ejpam-6331	151	16	⌝	⌝	PROPN
ejpam-6331	151	17	∗(	∗(	NOUN
ejpam-6331	151	18	⌜	⌜	PROPN
ejpam-6331	151	19	ϑ̃	ϑ̃	PROPN
ejpam-6331	151	20	⌝	⌝	PROPN
ejpam-6331	151	21	∗	∗	NOUN
ejpam-6331	151	22	⌜	⌜	PROPN
ejpam-6331	151	23	ϑ̃	ϑ̃	PROPN
ejpam-6331	151	24	⌝	⌝	PROPN
ejpam-6331	151	25	)	)	PUNCT
ejpam-6331	151	26	)	)	PUNCT
ejpam-6331	151	27	,	,	PUNCT
ejpam-6331	151	28	φ̃c(	φ̃c(	PROPN
ejpam-6331	151	29	⌜	⌜	PROPN
ejpam-6331	151	30	ϑ̃	ϑ̃	PROPN
ejpam-6331	151	31	⌝	⌝	PROPN
ejpam-6331	151	32	)e	)e	NOUN
ejpam-6331	151	33	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	151	34	⌜	⌜	PROPN
ejpam-6331	151	35	ϑ̃	ϑ̃	PROPN
ejpam-6331	151	36	⌝	⌝	PROPN
ejpam-6331	151	37	)	)	PUNCT
ejpam-6331	151	38	}	}	PUNCT
ejpam-6331	151	39	≤	≤	NUM
ejpam-6331	151	40	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	151	41	⌜	⌜	NOUN
ejpam-6331	151	42	ϱ̃	ϱ̃	PROPN
ejpam-6331	151	43	⌝	⌝	PROPN
ejpam-6331	151	44	∗	∗	NOUN
ejpam-6331	151	45	0)eiθ̃c(	0)eiθ̃c(	NUM
ejpam-6331	151	46	⌜	⌜	PROPN
ejpam-6331	151	47	ϱ̃	ϱ̃	PROPN
ejpam-6331	151	48	⌝	⌝	PROPN
ejpam-6331	151	49	∗0	∗0	PROPN
ejpam-6331	151	50	)	)	PUNCT
ejpam-6331	151	51	,	,	PUNCT
ejpam-6331	151	52	φ̃c(	φ̃c(	PROPN
ejpam-6331	151	53	⌜	⌜	PROPN
ejpam-6331	151	54	ϑ̃	ϑ̃	PROPN
ejpam-6331	151	55	⌝	⌝	PROPN
ejpam-6331	151	56	)e	)e	NOUN
ejpam-6331	151	57	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	151	58	⌜	⌜	PROPN
ejpam-6331	151	59	ϑ̃	ϑ̃	PROPN
ejpam-6331	151	60	⌝	⌝	PROPN
ejpam-6331	151	61	)	)	PUNCT
ejpam-6331	151	62	}	}	PUNCT
ejpam-6331	151	63	≤	≤	NUM
ejpam-6331	151	64	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	151	65	⌜	⌜	NOUN
ejpam-6331	151	66	ϱ̃	ϱ̃	PROPN
ejpam-6331	151	67	⌝	⌝	PROPN
ejpam-6331	151	68	)e	)e	NOUN
ejpam-6331	151	69	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	151	70	⌜	⌜	PROPN
ejpam-6331	151	71	ϱ̃	ϱ̃	PROPN
ejpam-6331	151	72	⌝	⌝	PROPN
ejpam-6331	151	73	)	)	PUNCT
ejpam-6331	151	74	,	,	PUNCT
ejpam-6331	151	75	φ̃c(	φ̃c(	PROPN
ejpam-6331	151	76	⌜	⌜	PROPN
ejpam-6331	151	77	ϑ̃	ϑ̃	PROPN
ejpam-6331	151	78	⌝	⌝	PROPN
ejpam-6331	151	79	)e	)e	NOUN
ejpam-6331	151	80	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	151	81	⌜	⌜	PROPN
ejpam-6331	151	82	ϑ̃	ϑ̃	PROPN
ejpam-6331	151	83	⌝	⌝	PROPN
ejpam-6331	151	84	)	)	PUNCT
ejpam-6331	151	85	}	}	PUNCT
ejpam-6331	151	86	.	.	PUNCT
ejpam-6331	152	1	(	(	PUNCT
ejpam-6331	152	2	4	4	X
ejpam-6331	152	3	)	)	PUNCT
ejpam-6331	152	4	using	use	VERB
ejpam-6331	152	5	bci-1	bci-1	PUNCT
ejpam-6331	152	6	and	and	CCONJ
ejpam-6331	152	7	(	(	PUNCT
ejpam-6331	152	8	1	1	X
ejpam-6331	152	9	)	)	PUNCT
ejpam-6331	152	10	above	above	ADV
ejpam-6331	152	11	,	,	PUNCT
ejpam-6331	152	12	we	we	PRON
ejpam-6331	152	13	have	have	VERB
ejpam-6331	152	14	∅̃c((	∅̃c((	PROPN
ejpam-6331	152	15	⌜	⌜	NOUN
ejpam-6331	152	16	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	17	⌝	⌝	PROPN
ejpam-6331	152	18	∗	∗	NOUN
ejpam-6331	152	19	⌜	⌜	PROPN
ejpam-6331	152	20	ϑ̃	ϑ̃	PROPN
ejpam-6331	152	21	⌝	⌝	PROPN
ejpam-6331	152	22	)	)	PUNCT
ejpam-6331	152	23	∗	∗	NOUN
ejpam-6331	152	24	(	(	PUNCT
ejpam-6331	152	25	⌜	⌜	NOUN
ejpam-6331	152	26	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	27	⌝	⌝	PROPN
ejpam-6331	152	28	∗	∗	NOUN
ejpam-6331	152	29	⌜	⌜	PROPN
ejpam-6331	152	30	κ̃	κ̃	PROPN
ejpam-6331	152	31	⌝	⌝	PROPN
ejpam-6331	152	32	))eiω̃c((	))eiω̃c((	PROPN
ejpam-6331	152	33	⌜	⌜	PROPN
ejpam-6331	152	34	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	35	⌝	⌝	PROPN
ejpam-6331	152	36	∗	∗	NOUN
ejpam-6331	152	37	⌜	⌜	PROPN
ejpam-6331	152	38	ϑ̃	ϑ̃	PROPN
ejpam-6331	152	39	⌝	⌝	PROPN
ejpam-6331	152	40	)∗(	)∗(	PROPN
ejpam-6331	152	41	⌜	⌜	PROPN
ejpam-6331	152	42	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	43	⌝	⌝	PROPN
ejpam-6331	152	44	∗	∗	NOUN
ejpam-6331	152	45	⌜	⌜	PROPN
ejpam-6331	152	46	κ̃	κ̃	PROPN
ejpam-6331	152	47	⌝	⌝	PROPN
ejpam-6331	152	48	)	)	PUNCT
ejpam-6331	152	49	≥	≥	NOUN
ejpam-6331	152	50	∅̃c(	∅̃c(	NOUN
ejpam-6331	152	51	⌜	⌜	NOUN
ejpam-6331	152	52	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	53	⌝	⌝	PROPN
ejpam-6331	152	54	∗	∗	NOUN
ejpam-6331	152	55	⌜	⌜	PROPN
ejpam-6331	152	56	ϑ̃	ϑ̃	PROPN
ejpam-6331	152	57	⌝	⌝	PROPN
ejpam-6331	152	58	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	152	59	⌜	⌜	PROPN
ejpam-6331	152	60	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	61	⌝	⌝	PROPN
ejpam-6331	152	62	∗	∗	NOUN
ejpam-6331	152	63	⌜	⌜	PROPN
ejpam-6331	152	64	ϑ̃	ϑ̃	PROPN
ejpam-6331	152	65	⌝	⌝	PROPN
ejpam-6331	152	66	)	)	PUNCT
ejpam-6331	152	67	and	and	CCONJ
ejpam-6331	152	68	φ̃c((	φ̃c((	ADP
ejpam-6331	152	69	⌜	⌜	NOUN
ejpam-6331	152	70	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	71	⌝	⌝	PROPN
ejpam-6331	152	72	∗	∗	NOUN
ejpam-6331	152	73	⌜	⌜	PROPN
ejpam-6331	152	74	ϑ̃	ϑ̃	PROPN
ejpam-6331	152	75	⌝	⌝	PROPN
ejpam-6331	152	76	)	)	PUNCT
ejpam-6331	152	77	∗	∗	NOUN
ejpam-6331	152	78	(	(	PUNCT
ejpam-6331	152	79	⌜	⌜	NOUN
ejpam-6331	152	80	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	81	⌝	⌝	PROPN
ejpam-6331	152	82	∗	∗	NOUN
ejpam-6331	152	83	⌜	⌜	PROPN
ejpam-6331	152	84	κ̃	κ̃	PROPN
ejpam-6331	152	85	⌝	⌝	PROPN
ejpam-6331	152	86	))eiω̃c((	))eiω̃c((	PROPN
ejpam-6331	152	87	⌜	⌜	PROPN
ejpam-6331	152	88	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	89	⌝	⌝	PROPN
ejpam-6331	152	90	∗	∗	NOUN
ejpam-6331	152	91	⌜	⌜	PROPN
ejpam-6331	152	92	ϑ̃	ϑ̃	PROPN
ejpam-6331	152	93	⌝	⌝	PROPN
ejpam-6331	152	94	)∗(	)∗(	PROPN
ejpam-6331	152	95	⌜	⌜	PROPN
ejpam-6331	152	96	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	97	⌝	⌝	PROPN
ejpam-6331	152	98	∗	∗	NOUN
ejpam-6331	152	99	⌜	⌜	PROPN
ejpam-6331	152	100	κ̃	κ̃	PROPN
ejpam-6331	152	101	⌝	⌝	PROPN
ejpam-6331	152	102	)	)	PUNCT
ejpam-6331	152	103	≤	≤	NOUN
ejpam-6331	152	104	φ̃c(	φ̃c(	NOUN
ejpam-6331	152	105	⌜	⌜	NOUN
ejpam-6331	152	106	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	107	⌝	⌝	PROPN
ejpam-6331	152	108	∗	∗	NOUN
ejpam-6331	152	109	⌜	⌜	PROPN
ejpam-6331	152	110	ϑ̃	ϑ̃	PROPN
ejpam-6331	152	111	⌝	⌝	PROPN
ejpam-6331	152	112	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	152	113	⌜	⌜	PROPN
ejpam-6331	152	114	ϱ̃	ϱ̃	PROPN
ejpam-6331	152	115	⌝	⌝	PROPN
ejpam-6331	152	116	∗	∗	NOUN
ejpam-6331	152	117	⌜	⌜	PROPN
ejpam-6331	152	118	ϑ̃	ϑ̃	PROPN
ejpam-6331	152	119	⌝	⌝	PROPN
ejpam-6331	152	120	)	)	PUNCT
ejpam-6331	152	121	.	.	PUNCT
ejpam-6331	153	1	by	by	ADP
ejpam-6331	153	2	using	use	VERB
ejpam-6331	153	3	theorem	theorem	NOUN
ejpam-6331	153	4	1	1	NUM
ejpam-6331	153	5	,	,	PUNCT
ejpam-6331	153	6	we	we	PRON
ejpam-6331	153	7	have	have	VERB
ejpam-6331	153	8	∅̃c(	∅̃c(	NOUN
ejpam-6331	153	9	⌜	⌜	NOUN
ejpam-6331	153	10	ϱ̃	ϱ̃	PROPN
ejpam-6331	153	11	⌝	⌝	PROPN
ejpam-6331	153	12	∗	∗	NOUN
ejpam-6331	153	13	⌜	⌜	PROPN
ejpam-6331	153	14	ϑ̃	ϑ̃	PROPN
ejpam-6331	153	15	⌝	⌝	PROPN
ejpam-6331	153	16	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	153	17	⌜	⌜	PROPN
ejpam-6331	153	18	ϱ̃	ϱ̃	PROPN
ejpam-6331	153	19	⌝	⌝	PROPN
ejpam-6331	153	20	∗	∗	NOUN
ejpam-6331	153	21	⌜	⌜	PROPN
ejpam-6331	153	22	ϑ̃	ϑ̃	PROPN
ejpam-6331	153	23	⌝	⌝	PROPN
ejpam-6331	153	24	)	)	PUNCT
ejpam-6331	153	25	≥	≥	PROPN
ejpam-6331	153	26	min{∅̃c((	min{∅̃c((	PROPN
ejpam-6331	153	27	⌜	⌜	PROPN
ejpam-6331	153	28	ϱ̃	ϱ̃	PROPN
ejpam-6331	153	29	⌝	⌝	PROPN
ejpam-6331	153	30	∗	∗	NOUN
ejpam-6331	153	31	⌜	⌜	PROPN
ejpam-6331	153	32	ϑ̃	ϑ̃	PROPN
ejpam-6331	153	33	⌝	⌝	PROPN
ejpam-6331	153	34	)	)	PUNCT
ejpam-6331	153	35	∗	∗	NOUN
ejpam-6331	153	36	(	(	PUNCT
ejpam-6331	153	37	⌜	⌜	NOUN
ejpam-6331	153	38	ϱ̃	ϱ̃	PROPN
ejpam-6331	153	39	⌝	⌝	PROPN
ejpam-6331	153	40	∗	∗	NOUN
ejpam-6331	153	41	⌜	⌜	PROPN
ejpam-6331	153	42	κ̃	κ̃	PROPN
ejpam-6331	153	43	⌝	⌝	PROPN
ejpam-6331	153	44	))eiω̃c((	))eiω̃c((	PROPN
ejpam-6331	153	45	⌜	⌜	PROPN
ejpam-6331	153	46	ϱ̃	ϱ̃	PROPN
ejpam-6331	153	47	⌝	⌝	PROPN
ejpam-6331	153	48	∗	∗	NOUN
ejpam-6331	153	49	⌜	⌜	PROPN
ejpam-6331	153	50	ϑ̃	ϑ̃	PROPN
ejpam-6331	153	51	⌝	⌝	PROPN
ejpam-6331	153	52	)∗(	)∗(	PROPN
ejpam-6331	153	53	⌜	⌜	PROPN
ejpam-6331	153	54	ϱ̃	ϱ̃	PROPN
ejpam-6331	153	55	⌝	⌝	PROPN
ejpam-6331	153	56	∗	∗	NOUN
ejpam-6331	153	57	⌜	⌜	PROPN
ejpam-6331	153	58	κ̃	κ̃	PROPN
ejpam-6331	153	59	⌝	⌝	PROPN
ejpam-6331	153	60	)	)	PUNCT
ejpam-6331	153	61	,	,	PUNCT
ejpam-6331	153	62	∅̃c(	∅̃c(	NOUN
ejpam-6331	153	63	⌜	⌜	SYM
ejpam-6331	153	64	ϱ̃	ϱ̃	PROPN
ejpam-6331	153	65	⌝	⌝	PROPN
ejpam-6331	153	66	∗	∗	NOUN
ejpam-6331	153	67	⌜	⌜	PROPN
ejpam-6331	153	68	ϑ̃	ϑ̃	PROPN
ejpam-6331	153	69	⌝	⌝	PROPN
ejpam-6331	153	70	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	153	71	⌜	⌜	PROPN
ejpam-6331	153	72	ϱ̃	ϱ̃	PROPN
ejpam-6331	153	73	⌝	⌝	PROPN
ejpam-6331	153	74	∗	∗	NOUN
ejpam-6331	153	75	⌜	⌜	PROPN
ejpam-6331	153	76	ϑ̃	ϑ̃	PROPN
ejpam-6331	153	77	⌝	⌝	PROPN
ejpam-6331	153	78	)	)	PUNCT
ejpam-6331	153	79	}	}	PUNCT
ejpam-6331	153	80	≥	≥	VERB
ejpam-6331	154	1	min{∅̃c(	min{∅̃c(	PRON
ejpam-6331	154	2	⌜	⌜	PROPN
ejpam-6331	154	3	ϱ̃	ϱ̃	PROPN
ejpam-6331	154	4	⌝	⌝	PROPN
ejpam-6331	154	5	∗	∗	NOUN
ejpam-6331	154	6	⌜	⌜	PROPN
ejpam-6331	154	7	ϑ̃	ϑ̃	PROPN
ejpam-6331	154	8	⌝	⌝	PROPN
ejpam-6331	154	9	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	154	10	⌜	⌜	PROPN
ejpam-6331	155	1	ϱ̃	ϱ̃	PROPN
ejpam-6331	155	2	⌝	⌝	PROPN
ejpam-6331	155	3	∗	∗	NOUN
ejpam-6331	155	4	⌜	⌜	PROPN
ejpam-6331	155	5	ϑ̃	ϑ̃	PROPN
ejpam-6331	155	6	⌝	⌝	PROPN
ejpam-6331	155	7	)	)	PUNCT
ejpam-6331	155	8	,	,	PUNCT
ejpam-6331	155	9	∅̃c(	∅̃c(	NOUN
ejpam-6331	155	10	⌜	⌜	SYM
ejpam-6331	155	11	ϱ̃	ϱ̃	PROPN
ejpam-6331	155	12	⌝	⌝	PROPN
ejpam-6331	155	13	∗	∗	NOUN
ejpam-6331	155	14	⌜	⌜	PROPN
ejpam-6331	155	15	κ̃	κ̃	PROPN
ejpam-6331	155	16	⌝	⌝	PROPN
ejpam-6331	155	17	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	155	18	⌜	⌜	PROPN
ejpam-6331	155	19	ϱ̃	ϱ̃	PROPN
ejpam-6331	155	20	⌝	⌝	PROPN
ejpam-6331	155	21	∗	∗	NOUN
ejpam-6331	155	22	⌜	⌜	PROPN
ejpam-6331	155	23	κ̃	κ̃	PROPN
ejpam-6331	155	24	⌝	⌝	PROPN
ejpam-6331	155	25	)	)	PUNCT
ejpam-6331	155	26	}	}	PUNCT
ejpam-6331	155	27	and	and	CCONJ
ejpam-6331	155	28	φ̃c(	φ̃c(	PROPN
ejpam-6331	155	29	⌜	⌜	NOUN
ejpam-6331	155	30	ϱ̃	ϱ̃	PROPN
ejpam-6331	155	31	⌝	⌝	PROPN
ejpam-6331	155	32	∗	∗	NOUN
ejpam-6331	155	33	⌜	⌜	PROPN
ejpam-6331	155	34	ϑ̃	ϑ̃	PROPN
ejpam-6331	155	35	⌝	⌝	PROPN
ejpam-6331	155	36	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	155	37	⌜	⌜	PROPN
ejpam-6331	155	38	ϱ̃	ϱ̃	PROPN
ejpam-6331	155	39	⌝	⌝	PROPN
ejpam-6331	155	40	∗	∗	NOUN
ejpam-6331	155	41	⌜	⌜	PROPN
ejpam-6331	155	42	ϑ̃	ϑ̃	PROPN
ejpam-6331	155	43	⌝	⌝	PROPN
ejpam-6331	155	44	)	)	PUNCT
ejpam-6331	155	45	≤	≤	PUNCT
ejpam-6331	156	1	max{φ̃c((	max{φ̃c((	PROPN
ejpam-6331	156	2	⌜	⌜	PROPN
ejpam-6331	156	3	ϱ̃	ϱ̃	PROPN
ejpam-6331	156	4	⌝	⌝	PROPN
ejpam-6331	156	5	∗	∗	NOUN
ejpam-6331	156	6	⌜	⌜	PROPN
ejpam-6331	156	7	ϑ̃	ϑ̃	PROPN
ejpam-6331	156	8	⌝	⌝	PROPN
ejpam-6331	156	9	)	)	PUNCT
ejpam-6331	156	10	∗	∗	NOUN
ejpam-6331	156	11	(	(	PUNCT
ejpam-6331	156	12	⌜	⌜	NOUN
ejpam-6331	156	13	ϱ̃	ϱ̃	PROPN
ejpam-6331	156	14	⌝	⌝	PROPN
ejpam-6331	156	15	∗	∗	NOUN
ejpam-6331	156	16	⌜	⌜	PROPN
ejpam-6331	156	17	κ̃	κ̃	PROPN
ejpam-6331	156	18	⌝	⌝	PROPN
ejpam-6331	156	19	)eiθ̃c((	)eiθ̃c((	NOUN
ejpam-6331	156	20	⌜	⌜	PROPN
ejpam-6331	156	21	ϱ̃	ϱ̃	PROPN
ejpam-6331	156	22	⌝	⌝	PROPN
ejpam-6331	156	23	∗	∗	NOUN
ejpam-6331	156	24	⌜	⌜	PROPN
ejpam-6331	156	25	ϑ̃	ϑ̃	PROPN
ejpam-6331	156	26	⌝	⌝	PROPN
ejpam-6331	156	27	)∗(	)∗(	PROPN
ejpam-6331	156	28	⌜	⌜	PROPN
ejpam-6331	156	29	ϱ̃	ϱ̃	PROPN
ejpam-6331	156	30	⌝	⌝	PROPN
ejpam-6331	156	31	∗	∗	NOUN
ejpam-6331	156	32	⌜	⌜	PROPN
ejpam-6331	156	33	κ̃	κ̃	PROPN
ejpam-6331	156	34	⌝	⌝	PROPN
ejpam-6331	156	35	)	)	PUNCT
ejpam-6331	156	36	,	,	PUNCT
ejpam-6331	156	37	φ̃c(	φ̃c(	VERB
ejpam-6331	156	38	⌜	⌜	NOUN
ejpam-6331	156	39	ϱ̃	ϱ̃	PROPN
ejpam-6331	156	40	⌝	⌝	PROPN
ejpam-6331	156	41	∗	∗	NOUN
ejpam-6331	156	42	⌜	⌜	PROPN
ejpam-6331	156	43	κ̃	κ̃	PROPN
ejpam-6331	156	44	⌝	⌝	PROPN
ejpam-6331	156	45	)eiθ̃c(	)eiθ̃c(	ADJ
ejpam-6331	156	46	⌜	⌜	PROPN
ejpam-6331	156	47	ϱ̃	ϱ̃	PROPN
ejpam-6331	156	48	⌝	⌝	PROPN
ejpam-6331	156	49	∗	∗	NOUN
ejpam-6331	156	50	⌜	⌜	PROPN
ejpam-6331	156	51	κ̃	κ̃	PROPN
ejpam-6331	156	52	⌝	⌝	PROPN
ejpam-6331	156	53	)	)	PUNCT
ejpam-6331	156	54	}	}	PUNCT
ejpam-6331	156	55	≤	≤	NUM
ejpam-6331	156	56	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	156	57	⌜	⌜	NOUN
ejpam-6331	156	58	ϱ̃	ϱ̃	PROPN
ejpam-6331	156	59	⌝	⌝	PROPN
ejpam-6331	156	60	∗	∗	NOUN
ejpam-6331	156	61	⌜	⌜	PROPN
ejpam-6331	156	62	ϑ̃	ϑ̃	PROPN
ejpam-6331	156	63	⌝	⌝	PROPN
ejpam-6331	156	64	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	156	65	⌜	⌜	PROPN
ejpam-6331	156	66	ϱ̃	ϱ̃	PROPN
ejpam-6331	156	67	⌝	⌝	PROPN
ejpam-6331	156	68	∗	∗	NOUN
ejpam-6331	156	69	⌜	⌜	PROPN
ejpam-6331	156	70	ϑ̃	ϑ̃	PROPN
ejpam-6331	156	71	⌝	⌝	PROPN
ejpam-6331	156	72	)	)	PUNCT
ejpam-6331	156	73	,	,	PUNCT
ejpam-6331	156	74	φ̃c(	φ̃c(	VERB
ejpam-6331	156	75	⌜	⌜	NOUN
ejpam-6331	156	76	ϱ̃	ϱ̃	PROPN
ejpam-6331	156	77	⌝	⌝	PROPN
ejpam-6331	156	78	∗	∗	NOUN
ejpam-6331	156	79	⌜	⌜	PROPN
ejpam-6331	156	80	κ̃	κ̃	PROPN
ejpam-6331	156	81	⌝	⌝	PROPN
ejpam-6331	156	82	)eiθ̃c(	)eiθ̃c(	ADJ
ejpam-6331	156	83	⌜	⌜	PROPN
ejpam-6331	156	84	ϱ̃	ϱ̃	PROPN
ejpam-6331	156	85	⌝	⌝	PROPN
ejpam-6331	156	86	∗	∗	NOUN
ejpam-6331	156	87	⌜	⌜	PROPN
ejpam-6331	156	88	κ̃	κ̃	PROPN
ejpam-6331	156	89	⌝	⌝	PROPN
ejpam-6331	156	90	)	)	PUNCT
ejpam-6331	156	91	}	}	PUNCT
ejpam-6331	156	92	.	.	PUNCT
ejpam-6331	157	1	(	(	PUNCT
ejpam-6331	157	2	5	5	X
ejpam-6331	157	3	)	)	PUNCT
ejpam-6331	157	4	put	put	VERB
ejpam-6331	157	5	⌜	⌜	PROPN
ejpam-6331	157	6	ϱ̃	ϱ̃	PROPN
ejpam-6331	157	7	⌝	⌝	NOUN
ejpam-6331	157	8	=	=	SYM
ejpam-6331	157	9	0	0	NUM
ejpam-6331	157	10	∗	∗	NOUN
ejpam-6331	157	11	⌜	⌜	PROPN
ejpam-6331	157	12	ϱ̃	ϱ̃	PROPN
ejpam-6331	157	13	⌝	⌝	PROPN
ejpam-6331	157	14	,	,	PUNCT
ejpam-6331	157	15	⌜	⌜	PROPN
ejpam-6331	157	16	ϑ̃	ϑ̃	PROPN
ejpam-6331	157	17	⌝	⌝	PROPN
ejpam-6331	157	18	=	=	SYM
ejpam-6331	157	19	0	0	NUM
ejpam-6331	157	20	,	,	PUNCT
ejpam-6331	157	21	⌜	⌜	PROPN
ejpam-6331	157	22	κ̃	κ̃	PROPN
ejpam-6331	157	23	⌝	⌝	PROPN
ejpam-6331	157	24	=	=	SYM
ejpam-6331	157	25	⌜	⌜	PROPN
ejpam-6331	157	26	ϱ̃	ϱ̃	PROPN
ejpam-6331	157	27	⌝	⌝	PROPN
ejpam-6331	157	28	in	in	ADP
ejpam-6331	157	29	cifqai-2	cifqai-2	NUM
ejpam-6331	157	30	and	and	CCONJ
ejpam-6331	157	31	cifqai-3	cifqai-3	NUM
ejpam-6331	157	32	,	,	PUNCT
ejpam-6331	157	33	we	we	PRON
ejpam-6331	157	34	have	have	VERB
ejpam-6331	157	35	∅̃c((0	∅̃c((0	PROPN
ejpam-6331	157	36	∗	∗	NOUN
ejpam-6331	157	37	⌜	⌜	PROPN
ejpam-6331	157	38	ϱ̃	ϱ̃	PROPN
ejpam-6331	157	39	⌝	⌝	PROPN
ejpam-6331	157	40	)	)	PUNCT
ejpam-6331	157	41	∗	∗	NOUN
ejpam-6331	157	42	⌜	⌜	PROPN
ejpam-6331	157	43	ϱ̃	ϱ̃	PROPN
ejpam-6331	157	44	⌝	⌝	PROPN
ejpam-6331	157	45	)eiω̃c((0∗	)eiω̃c((0∗	PROPN
ejpam-6331	157	46	⌜	⌜	PROPN
ejpam-6331	157	47	ϱ̃	ϱ̃	PROPN
ejpam-6331	157	48	⌝	⌝	PROPN
ejpam-6331	157	49	)∗	)∗	PROPN
ejpam-6331	157	50	⌜	⌜	PROPN
ejpam-6331	157	51	ϱ̃	ϱ̃	PROPN
ejpam-6331	157	52	⌝	⌝	PROPN
ejpam-6331	157	53	)	)	PUNCT
ejpam-6331	157	54	t.	t.	PROPN
ejpam-6331	157	55	ramesh	ramesh	PROPN
ejpam-6331	157	56	,	,	PUNCT
ejpam-6331	157	57	m.	m.	NOUN
ejpam-6331	157	58	balamurugan	balamurugan	PROPN
ejpam-6331	157	59	,	,	PUNCT
ejpam-6331	157	60	a.	a.	NOUN
ejpam-6331	157	61	iampan	iampan	PROPN
ejpam-6331	157	62	/	/	SYM
ejpam-6331	157	63	eur	eur	PROPN
ejpam-6331	157	64	.	.	PUNCT
ejpam-6331	158	1	j.	j.	PROPN
ejpam-6331	158	2	pure	pure	PROPN
ejpam-6331	158	3	appl	appl	PROPN
ejpam-6331	158	4	.	.	PROPN
ejpam-6331	158	5	math	math	PROPN
ejpam-6331	158	6	,	,	PUNCT
ejpam-6331	158	7	18	18	NUM
ejpam-6331	158	8	(	(	PUNCT
ejpam-6331	158	9	3	3	NUM
ejpam-6331	158	10	)	)	PUNCT
ejpam-6331	158	11	(	(	PUNCT
ejpam-6331	158	12	2025	2025	NUM
ejpam-6331	158	13	)	)	PUNCT
ejpam-6331	158	14	,	,	PUNCT
ejpam-6331	158	15	6331	6331	NUM
ejpam-6331	158	16	9	9	NUM
ejpam-6331	158	17	of	of	ADP
ejpam-6331	158	18	14	14	NUM
ejpam-6331	158	19	≥	≥	NOUN
ejpam-6331	158	20	min{∅̃c((0	min{∅̃c((0	PROPN
ejpam-6331	158	21	∗	∗	NOUN
ejpam-6331	158	22	⌜	⌜	PROPN
ejpam-6331	158	23	ϱ̃	ϱ̃	PROPN
ejpam-6331	158	24	⌝	⌝	PROPN
ejpam-6331	158	25	)	)	PUNCT
ejpam-6331	158	26	∗	∗	NOUN
ejpam-6331	158	27	(	(	PUNCT
ejpam-6331	158	28	0	0	NUM
ejpam-6331	158	29	∗	∗	NOUN
ejpam-6331	158	30	⌜	⌜	PROPN
ejpam-6331	158	31	ϱ̃	ϱ̃	PROPN
ejpam-6331	158	32	⌝	⌝	PROPN
ejpam-6331	158	33	))eiω̃c(0∗	))eiω̃c(0∗	PROPN
ejpam-6331	158	34	⌜	⌜	PROPN
ejpam-6331	158	35	ϱ̃	ϱ̃	PROPN
ejpam-6331	158	36	⌝	⌝	PROPN
ejpam-6331	158	37	)∗(0∗	)∗(0∗	PRON
ejpam-6331	158	38	⌜	⌜	PROPN
ejpam-6331	158	39	ϱ̃	ϱ̃	PROPN
ejpam-6331	158	40	⌝	⌝	PROPN
ejpam-6331	158	41	)	)	PUNCT
ejpam-6331	158	42	,	,	PUNCT
ejpam-6331	158	43	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	NOUN
ejpam-6331	158	44	)	)	PUNCT
ejpam-6331	158	45	}	}	PUNCT
ejpam-6331	158	46	=	=	SYM
ejpam-6331	158	47	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	X
ejpam-6331	158	48	)	)	PUNCT
ejpam-6331	158	49	and	and	CCONJ
ejpam-6331	158	50	φ̃c((0	φ̃c((0	ADP
ejpam-6331	158	51	∗	∗	NOUN
ejpam-6331	158	52	⌜	⌜	PROPN
ejpam-6331	158	53	ϱ̃	ϱ̃	PROPN
ejpam-6331	158	54	⌝	⌝	PROPN
ejpam-6331	158	55	)	)	PUNCT
ejpam-6331	158	56	∗	∗	NOUN
ejpam-6331	158	57	⌜	⌜	PROPN
ejpam-6331	158	58	ϱ̃	ϱ̃	PROPN
ejpam-6331	158	59	⌝	⌝	PROPN
ejpam-6331	158	60	)eiθ̃c((0∗	)eiθ̃c((0∗	PROPN
ejpam-6331	158	61	⌜	⌜	PROPN
ejpam-6331	158	62	ϱ̃	ϱ̃	PROPN
ejpam-6331	158	63	⌝	⌝	PROPN
ejpam-6331	158	64	)∗	)∗	PROPN
ejpam-6331	158	65	⌜	⌜	PROPN
ejpam-6331	158	66	ϱ̃	ϱ̃	PROPN
ejpam-6331	158	67	⌝	⌝	PROPN
ejpam-6331	158	68	)	)	PUNCT
ejpam-6331	158	69	≤	≤	PUNCT
ejpam-6331	159	1	max{φ̃c((0	max{φ̃c((0	PROPN
ejpam-6331	159	2	∗	∗	NOUN
ejpam-6331	159	3	⌜	⌜	PROPN
ejpam-6331	159	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	159	5	⌝	⌝	PROPN
ejpam-6331	159	6	)	)	PUNCT
ejpam-6331	159	7	∗	∗	NOUN
ejpam-6331	159	8	(	(	PUNCT
ejpam-6331	159	9	0	0	NUM
ejpam-6331	159	10	∗	∗	NOUN
ejpam-6331	159	11	⌜	⌜	PROPN
ejpam-6331	159	12	ϱ̃	ϱ̃	PROPN
ejpam-6331	159	13	⌝	⌝	PROPN
ejpam-6331	159	14	))eiθ̃c(0∗	))eiθ̃c(0∗	PROPN
ejpam-6331	159	15	⌜	⌜	PROPN
ejpam-6331	159	16	ϱ̃	ϱ̃	PROPN
ejpam-6331	159	17	⌝	⌝	PROPN
ejpam-6331	159	18	)∗(0∗	)∗(0∗	PRON
ejpam-6331	159	19	⌜	⌜	PROPN
ejpam-6331	159	20	ϱ̃	ϱ̃	PROPN
ejpam-6331	159	21	⌝	⌝	PROPN
ejpam-6331	159	22	)	)	PUNCT
ejpam-6331	159	23	,	,	PUNCT
ejpam-6331	160	1	φ̃c(0)e	φ̃c(0)e	NOUN
ejpam-6331	160	2	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	160	3	)	)	PUNCT
ejpam-6331	160	4	}	}	PUNCT
ejpam-6331	160	5	=	=	SYM
ejpam-6331	160	6	φ̃c(0)e	φ̃c(0)e	PRON
ejpam-6331	160	7	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	160	8	)	)	PUNCT
ejpam-6331	160	9	.	.	PUNCT
ejpam-6331	161	1	it	it	PRON
ejpam-6331	161	2	follows	follow	VERB
ejpam-6331	161	3	from	from	ADP
ejpam-6331	161	4	cifi-1	cifi-1	PROPN
ejpam-6331	161	5	that	that	PRON
ejpam-6331	161	6	∅̃c((0	∅̃c((0	VERB
ejpam-6331	161	7	∗	∗	NOUN
ejpam-6331	161	8	⌜	⌜	PROPN
ejpam-6331	161	9	ϱ̃	ϱ̃	PROPN
ejpam-6331	161	10	⌝	⌝	PROPN
ejpam-6331	161	11	)	)	PUNCT
ejpam-6331	161	12	∗	∗	NOUN
ejpam-6331	161	13	⌜	⌜	PROPN
ejpam-6331	161	14	ϱ̃	ϱ̃	PROPN
ejpam-6331	161	15	⌝	⌝	PROPN
ejpam-6331	161	16	)eiω̃c((0∗	)eiω̃c((0∗	PROPN
ejpam-6331	161	17	⌜	⌜	PROPN
ejpam-6331	161	18	ϱ̃	ϱ̃	PROPN
ejpam-6331	161	19	⌝	⌝	PROPN
ejpam-6331	161	20	)∗	)∗	PROPN
ejpam-6331	161	21	⌜	⌜	PROPN
ejpam-6331	161	22	ϱ̃	ϱ̃	PROPN
ejpam-6331	161	23	⌝	⌝	PROPN
ejpam-6331	161	24	)	)	PUNCT
ejpam-6331	161	25	=	=	SYM
ejpam-6331	161	26	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	X
ejpam-6331	161	27	)	)	PUNCT
ejpam-6331	161	28	and	and	CCONJ
ejpam-6331	161	29	φ̃c((0	φ̃c((0	ADP
ejpam-6331	161	30	∗	∗	NOUN
ejpam-6331	161	31	⌜	⌜	PROPN
ejpam-6331	161	32	ϱ̃	ϱ̃	PROPN
ejpam-6331	161	33	⌝	⌝	PROPN
ejpam-6331	161	34	)	)	PUNCT
ejpam-6331	161	35	∗	∗	NOUN
ejpam-6331	161	36	⌜	⌜	PROPN
ejpam-6331	161	37	ϱ̃	ϱ̃	PROPN
ejpam-6331	161	38	⌝	⌝	PROPN
ejpam-6331	161	39	)eiθ̃c((0∗	)eiθ̃c((0∗	PROPN
ejpam-6331	161	40	⌜	⌜	PROPN
ejpam-6331	161	41	ϱ̃	ϱ̃	PROPN
ejpam-6331	161	42	⌝	⌝	PROPN
ejpam-6331	161	43	)∗	)∗	PROPN
ejpam-6331	161	44	⌜	⌜	PROPN
ejpam-6331	161	45	ϱ̃	ϱ̃	PROPN
ejpam-6331	161	46	⌝	⌝	PROPN
ejpam-6331	161	47	)	)	PUNCT
ejpam-6331	161	48	=	=	PUNCT
ejpam-6331	161	49	φ̃c(0)e	φ̃c(0)e	PRON
ejpam-6331	161	50	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	161	51	)	)	PUNCT
ejpam-6331	161	52	.	.	PUNCT
ejpam-6331	162	1	remark	remark	PROPN
ejpam-6331	162	2	3	3	NUM
ejpam-6331	162	3	.	.	PUNCT
ejpam-6331	163	1	in	in	ADP
ejpam-6331	163	2	proposition	proposition	NOUN
ejpam-6331	163	3	1	1	NUM
ejpam-6331	163	4	,	,	PUNCT
ejpam-6331	163	5	every	every	DET
ejpam-6331	163	6	cifqa	cifqa	NOUN
ejpam-6331	163	7	-	-	PUNCT
ejpam-6331	163	8	ideal	ideal	NOUN
ejpam-6331	163	9	is	be	AUX
ejpam-6331	163	10	a	a	DET
ejpam-6331	163	11	cif	cif	PROPN
ejpam-6331	163	12	-	-	PUNCT
ejpam-6331	163	13	subalgebra	subalgebra	PROPN
ejpam-6331	163	14	.	.	PUNCT
ejpam-6331	164	1	proposition	proposition	NOUN
ejpam-6331	164	2	2	2	NUM
ejpam-6331	164	3	.	.	PUNCT
ejpam-6331	165	1	let	let	VERB
ejpam-6331	165	2	c	c	NOUN
ejpam-6331	165	3	=	=	SYM
ejpam-6331	165	4	(	(	PUNCT
ejpam-6331	165	5	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	165	6	,	,	PUNCT
ejpam-6331	165	7	φ̃ce	φ̃ce	PROPN
ejpam-6331	165	8	iθ̃c	iθ̃c	PROPN
ejpam-6331	165	9	)	)	PUNCT
ejpam-6331	165	10	be	be	VERB
ejpam-6331	165	11	a	a	DET
ejpam-6331	165	12	cif	cif	PROPN
ejpam-6331	165	13	-	-	PUNCT
ejpam-6331	165	14	ideal	ideal	NOUN
ejpam-6331	165	15	.	.	PUNCT
ejpam-6331	166	1	then	then	ADV
ejpam-6331	166	2	the	the	DET
ejpam-6331	166	3	following	follow	VERB
ejpam-6331	166	4	statements	statement	NOUN
ejpam-6331	166	5	are	be	AUX
ejpam-6331	166	6	equivalent	equivalent	ADJ
ejpam-6331	166	7	:	:	PUNCT
ejpam-6331	166	8	(	(	PUNCT
ejpam-6331	166	9	1	1	X
ejpam-6331	166	10	)	)	PUNCT
ejpam-6331	166	11	c	c	NOUN
ejpam-6331	166	12	=	=	SYM
ejpam-6331	166	13	(	(	PUNCT
ejpam-6331	166	14	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	166	15	,	,	PUNCT
ejpam-6331	166	16	φ̃ce	φ̃ce	PROPN
ejpam-6331	166	17	iθ̃c	iθ̃c	PROPN
ejpam-6331	166	18	)	)	PUNCT
ejpam-6331	166	19	is	be	AUX
ejpam-6331	166	20	a	a	DET
ejpam-6331	166	21	cifqa	cifqa	NOUN
ejpam-6331	166	22	-	-	PUNCT
ejpam-6331	166	23	ideal	ideal	NOUN
ejpam-6331	166	24	of	of	ADP
ejpam-6331	166	25	x	x	X
ejpam-6331	166	26	.	.	PUNCT
ejpam-6331	167	1	(	(	PUNCT
ejpam-6331	167	2	2	2	NUM
ejpam-6331	167	3	)	)	PUNCT
ejpam-6331	167	4	∅̃c(	∅̃c(	NOUN
ejpam-6331	167	5	⌜	⌜	PROPN
ejpam-6331	167	6	ϱ̃	ϱ̃	PROPN
ejpam-6331	167	7	⌝	⌝	PROPN
ejpam-6331	167	8	∗	∗	NOUN
ejpam-6331	167	9	⌜	⌜	PROPN
ejpam-6331	167	10	ϑ̃	ϑ̃	PROPN
ejpam-6331	167	11	⌝	⌝	PROPN
ejpam-6331	167	12	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	167	13	⌜	⌜	PROPN
ejpam-6331	167	14	ϱ̃	ϱ̃	PROPN
ejpam-6331	167	15	⌝	⌝	PROPN
ejpam-6331	167	16	∗	∗	NOUN
ejpam-6331	167	17	⌜	⌜	PROPN
ejpam-6331	167	18	ϑ̃	ϑ̃	PROPN
ejpam-6331	167	19	⌝	⌝	PROPN
ejpam-6331	167	20	)	)	PUNCT
ejpam-6331	167	21	≥	≥	NOUN
ejpam-6331	167	22	∅̃c(	∅̃c(	NOUN
ejpam-6331	167	23	⌜	⌜	NOUN
ejpam-6331	167	24	ϱ̃	ϱ̃	PROPN
ejpam-6331	167	25	⌝	⌝	PROPN
ejpam-6331	167	26	∗(0∗	∗(0∗	PROPN
ejpam-6331	167	27	⌜	⌜	PROPN
ejpam-6331	167	28	ϑ̃	ϑ̃	PROPN
ejpam-6331	167	29	⌝	⌝	PROPN
ejpam-6331	167	30	))eiω̃c(	))eiω̃c(	PROPN
ejpam-6331	167	31	⌜	⌜	PROPN
ejpam-6331	167	32	ϱ̃	ϱ̃	PROPN
ejpam-6331	167	33	⌝	⌝	PROPN
ejpam-6331	167	34	∗(0∗	∗(0∗	PROPN
ejpam-6331	167	35	⌜	⌜	PROPN
ejpam-6331	167	36	ϑ̃	ϑ̃	PROPN
ejpam-6331	167	37	⌝	⌝	PROPN
ejpam-6331	167	38	)	)	PUNCT
ejpam-6331	167	39	)	)	PUNCT
ejpam-6331	167	40	,	,	PUNCT
ejpam-6331	167	41	φ̃c(	φ̃c(	VERB
ejpam-6331	167	42	⌜	⌜	NOUN
ejpam-6331	167	43	ϱ̃	ϱ̃	PROPN
ejpam-6331	167	44	⌝	⌝	PROPN
ejpam-6331	167	45	∗	∗	NOUN
ejpam-6331	167	46	⌜	⌜	PROPN
ejpam-6331	167	47	ϑ̃	ϑ̃	PROPN
ejpam-6331	167	48	⌝	⌝	PROPN
ejpam-6331	167	49	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	167	50	⌜	⌜	PROPN
ejpam-6331	167	51	ϱ̃	ϱ̃	PROPN
ejpam-6331	167	52	⌝	⌝	PROPN
ejpam-6331	167	53	∗	∗	NOUN
ejpam-6331	167	54	⌜	⌜	PROPN
ejpam-6331	167	55	ϑ̃	ϑ̃	PROPN
ejpam-6331	167	56	⌝	⌝	PROPN
ejpam-6331	167	57	)	)	PUNCT
ejpam-6331	167	58	≤	≤	NOUN
ejpam-6331	167	59	φ̃c(	φ̃c(	NOUN
ejpam-6331	167	60	⌜	⌜	NOUN
ejpam-6331	167	61	ϱ̃	ϱ̃	PROPN
ejpam-6331	167	62	⌝	⌝	PROPN
ejpam-6331	167	63	∗	∗	NOUN
ejpam-6331	167	64	(	(	PUNCT
ejpam-6331	167	65	0	0	NUM
ejpam-6331	167	66	∗	∗	NOUN
ejpam-6331	167	67	⌜	⌜	PROPN
ejpam-6331	167	68	ϑ̃	ϑ̃	PROPN
ejpam-6331	167	69	⌝	⌝	PROPN
ejpam-6331	167	70	))eiθ̃c(	))eiθ̃c(	PROPN
ejpam-6331	167	71	⌜	⌜	PROPN
ejpam-6331	167	72	ϱ̃	ϱ̃	PROPN
ejpam-6331	167	73	⌝	⌝	PROPN
ejpam-6331	167	74	∗(0∗	∗(0∗	PROPN
ejpam-6331	167	75	⌜	⌜	PROPN
ejpam-6331	167	76	ϑ̃	ϑ̃	PROPN
ejpam-6331	167	77	⌝	⌝	PROPN
ejpam-6331	167	78	)	)	PUNCT
ejpam-6331	167	79	)	)	PUNCT
ejpam-6331	167	80	.	.	PUNCT
ejpam-6331	168	1	(	(	PUNCT
ejpam-6331	168	2	3	3	X
ejpam-6331	168	3	)	)	PUNCT
ejpam-6331	168	4	∅̃c((	∅̃c((	PROPN
ejpam-6331	168	5	⌜	⌜	PROPN
ejpam-6331	168	6	ϱ̃	ϱ̃	PROPN
ejpam-6331	168	7	⌝	⌝	PROPN
ejpam-6331	168	8	∗	∗	NOUN
ejpam-6331	168	9	⌜	⌜	PROPN
ejpam-6331	168	10	ϑ̃	ϑ̃	PROPN
ejpam-6331	168	11	⌝	⌝	PROPN
ejpam-6331	168	12	)	)	PUNCT
ejpam-6331	168	13	∗	∗	NOUN
ejpam-6331	168	14	⌜	⌜	PROPN
ejpam-6331	168	15	κ̃	κ̃	PROPN
ejpam-6331	168	16	⌝	⌝	PROPN
ejpam-6331	168	17	)eiω̃c((	)eiω̃c((	PROPN
ejpam-6331	168	18	⌜	⌜	PROPN
ejpam-6331	168	19	ϱ̃	ϱ̃	PROPN
ejpam-6331	168	20	⌝	⌝	PROPN
ejpam-6331	168	21	∗	∗	NOUN
ejpam-6331	168	22	⌜	⌜	PROPN
ejpam-6331	168	23	ϑ̃	ϑ̃	PROPN
ejpam-6331	168	24	⌝	⌝	PROPN
ejpam-6331	168	25	)∗	)∗	PROPN
ejpam-6331	168	26	⌜	⌜	PROPN
ejpam-6331	168	27	κ̃	κ̃	PROPN
ejpam-6331	168	28	⌝	⌝	PROPN
ejpam-6331	168	29	)	)	PUNCT
ejpam-6331	168	30	≥	≥	NOUN
ejpam-6331	168	31	∅̃c(l	∅̃c(l	NOUN
ejpam-6331	168	32	∗	∗	NOUN
ejpam-6331	168	33	(	(	PUNCT
ejpam-6331	168	34	m	m	PROPN
ejpam-6331	168	35	∗	∗	NOUN
ejpam-6331	168	36	n))eiω̃c(	n))eiω̃c(	PROPN
ejpam-6331	168	37	⌜	⌜	PROPN
ejpam-6331	168	38	ϱ̃	ϱ̃	PROPN
ejpam-6331	168	39	⌝	⌝	PROPN
ejpam-6331	168	40	∗	∗	NOUN
ejpam-6331	168	41	⌜	⌜	PROPN
ejpam-6331	168	42	ϑ̃	ϑ̃	PROPN
ejpam-6331	168	43	⌝	⌝	PROPN
ejpam-6331	168	44	)∗	)∗	PROPN
ejpam-6331	168	45	⌜	⌜	PROPN
ejpam-6331	168	46	κ̃	κ̃	PROPN
ejpam-6331	168	47	⌝	⌝	PROPN
ejpam-6331	168	48	)	)	PUNCT
ejpam-6331	168	49	)	)	PUNCT
ejpam-6331	168	50	,	,	PUNCT
ejpam-6331	168	51	φ̃c((	φ̃c((	PROPN
ejpam-6331	168	52	⌜	⌜	NOUN
ejpam-6331	168	53	ϱ̃	ϱ̃	PROPN
ejpam-6331	168	54	⌝	⌝	PROPN
ejpam-6331	168	55	∗	∗	NOUN
ejpam-6331	168	56	⌜	⌜	PROPN
ejpam-6331	168	57	ϑ̃	ϑ̃	PROPN
ejpam-6331	168	58	⌝	⌝	PROPN
ejpam-6331	168	59	)	)	PUNCT
ejpam-6331	168	60	∗	∗	NOUN
ejpam-6331	168	61	⌜	⌜	PROPN
ejpam-6331	168	62	κ̃	κ̃	PROPN
ejpam-6331	168	63	⌝	⌝	PROPN
ejpam-6331	168	64	)eiθ̃c((	)eiθ̃c((	NOUN
ejpam-6331	168	65	⌜	⌜	PROPN
ejpam-6331	168	66	ϱ̃	ϱ̃	PROPN
ejpam-6331	168	67	⌝	⌝	PROPN
ejpam-6331	168	68	∗	∗	NOUN
ejpam-6331	168	69	⌜	⌜	PROPN
ejpam-6331	168	70	ϑ̃	ϑ̃	PROPN
ejpam-6331	168	71	⌝	⌝	PROPN
ejpam-6331	168	72	)∗	)∗	PROPN
ejpam-6331	168	73	⌜	⌜	PROPN
ejpam-6331	168	74	κ̃	κ̃	PROPN
ejpam-6331	168	75	⌝	⌝	PROPN
ejpam-6331	168	76	)	)	PUNCT
ejpam-6331	168	77	≤	≤	NOUN
ejpam-6331	168	78	φ̃c(	φ̃c(	NOUN
ejpam-6331	168	79	⌜	⌜	NOUN
ejpam-6331	168	80	ϱ̃	ϱ̃	PROPN
ejpam-6331	168	81	⌝	⌝	PROPN
ejpam-6331	168	82	∗	∗	NOUN
ejpam-6331	168	83	⌜	⌜	PROPN
ejpam-6331	168	84	ϑ̃	ϑ̃	PROPN
ejpam-6331	168	85	⌝	⌝	PROPN
ejpam-6331	168	86	)	)	PUNCT
ejpam-6331	168	87	∗	∗	NOUN
ejpam-6331	168	88	⌜	⌜	PROPN
ejpam-6331	168	89	κ̃	κ̃	PROPN
ejpam-6331	168	90	⌝	⌝	PROPN
ejpam-6331	168	91	))eiθ̃c(	))eiθ̃c(	DET
ejpam-6331	168	92	⌜	⌜	PROPN
ejpam-6331	168	93	ϱ̃	ϱ̃	PROPN
ejpam-6331	168	94	⌝	⌝	PROPN
ejpam-6331	168	95	∗	∗	NOUN
ejpam-6331	168	96	⌜	⌜	PROPN
ejpam-6331	168	97	ϑ̃	ϑ̃	PROPN
ejpam-6331	168	98	⌝	⌝	PROPN
ejpam-6331	168	99	)∗	)∗	PROPN
ejpam-6331	168	100	⌜	⌜	PROPN
ejpam-6331	168	101	κ̃	κ̃	PROPN
ejpam-6331	168	102	⌝	⌝	PROPN
ejpam-6331	168	103	)	)	PUNCT
ejpam-6331	168	104	)	)	PUNCT
ejpam-6331	168	105	,	,	PUNCT
ejpam-6331	168	106	for	for	ADP
ejpam-6331	168	107	all	all	DET
ejpam-6331	168	108	⌜	⌜	PROPN
ejpam-6331	168	109	ϱ̃	ϱ̃	PROPN
ejpam-6331	168	110	⌝	⌝	PROPN
ejpam-6331	168	111	,	,	PUNCT
ejpam-6331	168	112	⌜	⌜	PROPN
ejpam-6331	168	113	ϑ̃	ϑ̃	PROPN
ejpam-6331	168	114	⌝	⌝	PROPN
ejpam-6331	168	115	,	,	PUNCT
ejpam-6331	168	116	⌜	⌜	PROPN
ejpam-6331	168	117	κ̃	κ̃	PROPN
ejpam-6331	168	118	⌝	⌝	PROPN
ejpam-6331	168	119	∈	∈	PROPN
ejpam-6331	168	120	x	x	X
ejpam-6331	168	121	.	.	PUNCT
ejpam-6331	169	1	proof	proof	NOUN
ejpam-6331	169	2	.	.	PUNCT
ejpam-6331	170	1	(	(	PUNCT
ejpam-6331	170	2	1	1	X
ejpam-6331	170	3	)	)	PUNCT
ejpam-6331	170	4	⇒	⇒	NOUN
ejpam-6331	170	5	(	(	PUNCT
ejpam-6331	170	6	2	2	X
ejpam-6331	170	7	)	)	PUNCT
ejpam-6331	170	8	assume	assume	VERB
ejpam-6331	170	9	that	that	SCONJ
ejpam-6331	170	10	c	c	AUX
ejpam-6331	170	11	=	=	SYM
ejpam-6331	170	12	(	(	PUNCT
ejpam-6331	170	13	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	170	14	,	,	PUNCT
ejpam-6331	170	15	φ̃ce	φ̃ce	PROPN
ejpam-6331	170	16	iθ̃c	iθ̃c	PROPN
ejpam-6331	170	17	)	)	PUNCT
ejpam-6331	170	18	is	be	AUX
ejpam-6331	170	19	a	a	DET
ejpam-6331	170	20	cifqa	cifqa	NOUN
ejpam-6331	170	21	-	-	PUNCT
ejpam-6331	170	22	ideal	ideal	NOUN
ejpam-6331	170	23	.	.	PUNCT
ejpam-6331	171	1	then	then	ADV
ejpam-6331	171	2	by	by	ADP
ejpam-6331	171	3	using	use	VERB
ejpam-6331	171	4	cifi-1	cifi-1	NUM
ejpam-6331	171	5	,	,	PUNCT
ejpam-6331	171	6	cifqai-1	cifqai-1	NUM
ejpam-6331	171	7	and	and	CCONJ
ejpam-6331	171	8	cifqai-2	cifqai-2	NUM
ejpam-6331	171	9	,	,	PUNCT
ejpam-6331	171	10	we	we	PRON
ejpam-6331	171	11	have	have	VERB
ejpam-6331	171	12	∅̃c(	∅̃c(	NOUN
ejpam-6331	171	13	⌜	⌜	NOUN
ejpam-6331	171	14	ϱ̃	ϱ̃	PROPN
ejpam-6331	171	15	⌝	⌝	PROPN
ejpam-6331	171	16	∗	∗	NOUN
ejpam-6331	171	17	⌜	⌜	PROPN
ejpam-6331	171	18	ϑ̃	ϑ̃	PROPN
ejpam-6331	171	19	⌝	⌝	PROPN
ejpam-6331	171	20	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	171	21	⌜	⌜	PROPN
ejpam-6331	171	22	ϱ̃	ϱ̃	PROPN
ejpam-6331	171	23	⌝	⌝	PROPN
ejpam-6331	171	24	∗	∗	NOUN
ejpam-6331	171	25	⌜	⌜	PROPN
ejpam-6331	171	26	ϑ̃	ϑ̃	PROPN
ejpam-6331	171	27	⌝	⌝	PROPN
ejpam-6331	171	28	)	)	PUNCT
ejpam-6331	171	29	≥	≥	NOUN
ejpam-6331	172	1	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	172	2	⌜	⌜	PROPN
ejpam-6331	172	3	ϱ̃	ϱ̃	PROPN
ejpam-6331	172	4	⌝	⌝	PROPN
ejpam-6331	172	5	∗	∗	NOUN
ejpam-6331	172	6	(	(	PUNCT
ejpam-6331	172	7	0	0	NUM
ejpam-6331	172	8	∗	∗	NOUN
ejpam-6331	172	9	⌜	⌜	PROPN
ejpam-6331	172	10	ϑ̃	ϑ̃	PROPN
ejpam-6331	172	11	⌝	⌝	PROPN
ejpam-6331	172	12	))eiω̃c(	))eiω̃c(	PROPN
ejpam-6331	172	13	⌜	⌜	PROPN
ejpam-6331	172	14	ϱ̃	ϱ̃	PROPN
ejpam-6331	172	15	⌝	⌝	PROPN
ejpam-6331	172	16	∗(0∗	∗(0∗	PROPN
ejpam-6331	172	17	⌜	⌜	PROPN
ejpam-6331	172	18	ϑ̃	ϑ̃	PROPN
ejpam-6331	172	19	⌝	⌝	PROPN
ejpam-6331	172	20	)	)	PUNCT
ejpam-6331	172	21	)	)	PUNCT
ejpam-6331	173	1	,	,	PUNCT
ejpam-6331	173	2	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	NOUN
ejpam-6331	173	3	)	)	PUNCT
ejpam-6331	173	4	}	}	PUNCT
ejpam-6331	173	5	≥	≥	NUM
ejpam-6331	173	6	∅̃c(	∅̃c(	NOUN
ejpam-6331	173	7	⌜	⌜	NOUN
ejpam-6331	173	8	ϱ̃	ϱ̃	PROPN
ejpam-6331	173	9	⌝	⌝	PROPN
ejpam-6331	173	10	∗	∗	NOUN
ejpam-6331	173	11	(	(	PUNCT
ejpam-6331	173	12	0	0	NUM
ejpam-6331	173	13	∗	∗	NOUN
ejpam-6331	173	14	⌜	⌜	PROPN
ejpam-6331	173	15	ϑ̃	ϑ̃	PROPN
ejpam-6331	173	16	⌝	⌝	PROPN
ejpam-6331	173	17	))eiω̃c(	))eiω̃c(	PROPN
ejpam-6331	173	18	⌜	⌜	PROPN
ejpam-6331	173	19	ϱ̃	ϱ̃	PROPN
ejpam-6331	173	20	⌝	⌝	PROPN
ejpam-6331	173	21	∗(0∗	∗(0∗	PROPN
ejpam-6331	173	22	⌜	⌜	PROPN
ejpam-6331	173	23	ϑ̃	ϑ̃	PROPN
ejpam-6331	173	24	⌝	⌝	PROPN
ejpam-6331	173	25	)	)	PUNCT
ejpam-6331	173	26	)	)	PUNCT
ejpam-6331	173	27	and	and	CCONJ
ejpam-6331	173	28	φ̃c(	φ̃c(	PROPN
ejpam-6331	173	29	⌜	⌜	NOUN
ejpam-6331	173	30	ϱ̃	ϱ̃	PROPN
ejpam-6331	173	31	⌝	⌝	PROPN
ejpam-6331	173	32	∗	∗	NOUN
ejpam-6331	173	33	⌜	⌜	PROPN
ejpam-6331	173	34	ϑ̃	ϑ̃	PROPN
ejpam-6331	173	35	⌝	⌝	PROPN
ejpam-6331	173	36	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	173	37	⌜	⌜	PROPN
ejpam-6331	173	38	ϱ̃	ϱ̃	PROPN
ejpam-6331	173	39	⌝	⌝	PROPN
ejpam-6331	173	40	∗	∗	NOUN
ejpam-6331	173	41	⌜	⌜	PROPN
ejpam-6331	173	42	ϑ̃	ϑ̃	PROPN
ejpam-6331	173	43	⌝	⌝	PROPN
ejpam-6331	173	44	)	)	PUNCT
ejpam-6331	173	45	≤	≤	NOUN
ejpam-6331	173	46	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	174	1	⌜	⌜	PROPN
ejpam-6331	174	2	ϱ̃	ϱ̃	PROPN
ejpam-6331	174	3	⌝	⌝	PROPN
ejpam-6331	174	4	∗	∗	NOUN
ejpam-6331	174	5	(	(	PUNCT
ejpam-6331	174	6	0	0	NUM
ejpam-6331	174	7	∗	∗	NOUN
ejpam-6331	174	8	⌜	⌜	PROPN
ejpam-6331	174	9	ϑ̃	ϑ̃	PROPN
ejpam-6331	174	10	⌝	⌝	PROPN
ejpam-6331	174	11	))eiθ̃c(	))eiθ̃c(	PROPN
ejpam-6331	174	12	⌜	⌜	PROPN
ejpam-6331	174	13	ϱ̃	ϱ̃	PROPN
ejpam-6331	174	14	⌝	⌝	PROPN
ejpam-6331	174	15	∗(0∗	∗(0∗	PROPN
ejpam-6331	174	16	⌜	⌜	PROPN
ejpam-6331	174	17	ϑ̃	ϑ̃	PROPN
ejpam-6331	174	18	⌝	⌝	PROPN
ejpam-6331	174	19	)	)	PUNCT
ejpam-6331	174	20	)	)	PUNCT
ejpam-6331	174	21	,	,	PUNCT
ejpam-6331	174	22	φ̃c(0)e	φ̃c(0)e	NOUN
ejpam-6331	174	23	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	174	24	)	)	PUNCT
ejpam-6331	174	25	}	}	PUNCT
ejpam-6331	174	26	≤	≤	NUM
ejpam-6331	174	27	φ̃c(	φ̃c(	NOUN
ejpam-6331	174	28	⌜	⌜	NOUN
ejpam-6331	174	29	ϱ̃	ϱ̃	PROPN
ejpam-6331	174	30	⌝	⌝	PROPN
ejpam-6331	174	31	∗	∗	NOUN
ejpam-6331	174	32	(	(	PUNCT
ejpam-6331	174	33	0	0	NUM
ejpam-6331	174	34	∗	∗	NOUN
ejpam-6331	174	35	⌜	⌜	PROPN
ejpam-6331	174	36	ϑ̃	ϑ̃	PROPN
ejpam-6331	174	37	⌝	⌝	PROPN
ejpam-6331	174	38	))eiθ̃c(	))eiθ̃c(	PROPN
ejpam-6331	174	39	⌜	⌜	PROPN
ejpam-6331	174	40	ϱ̃	ϱ̃	PROPN
ejpam-6331	174	41	⌝	⌝	PROPN
ejpam-6331	174	42	∗(0∗	∗(0∗	PROPN
ejpam-6331	174	43	⌜	⌜	PROPN
ejpam-6331	174	44	ϑ̃	ϑ̃	PROPN
ejpam-6331	174	45	⌝	⌝	PROPN
ejpam-6331	174	46	)	)	PUNCT
ejpam-6331	174	47	)	)	PUNCT
ejpam-6331	174	48	.	.	PUNCT
ejpam-6331	175	1	t.	t.	PROPN
ejpam-6331	175	2	ramesh	ramesh	PROPN
ejpam-6331	175	3	,	,	PUNCT
ejpam-6331	175	4	m.	m.	NOUN
ejpam-6331	175	5	balamurugan	balamurugan	PROPN
ejpam-6331	175	6	,	,	PUNCT
ejpam-6331	175	7	a.	a.	NOUN
ejpam-6331	175	8	iampan	iampan	PROPN
ejpam-6331	175	9	/	/	SYM
ejpam-6331	175	10	eur	eur	PROPN
ejpam-6331	175	11	.	.	PUNCT
ejpam-6331	176	1	j.	j.	PROPN
ejpam-6331	176	2	pure	pure	PROPN
ejpam-6331	176	3	appl	appl	PROPN
ejpam-6331	176	4	.	.	PROPN
ejpam-6331	176	5	math	math	PROPN
ejpam-6331	176	6	,	,	PUNCT
ejpam-6331	176	7	18	18	NUM
ejpam-6331	176	8	(	(	PUNCT
ejpam-6331	176	9	3	3	NUM
ejpam-6331	176	10	)	)	PUNCT
ejpam-6331	176	11	(	(	PUNCT
ejpam-6331	176	12	2025	2025	NUM
ejpam-6331	176	13	)	)	PUNCT
ejpam-6331	176	14	,	,	PUNCT
ejpam-6331	176	15	6331	6331	NUM
ejpam-6331	176	16	10	10	NUM
ejpam-6331	176	17	of	of	ADP
ejpam-6331	176	18	14	14	NUM
ejpam-6331	176	19	hence	hence	ADV
ejpam-6331	176	20	,	,	PUNCT
ejpam-6331	176	21	(	(	PUNCT
ejpam-6331	176	22	2	2	X
ejpam-6331	176	23	)	)	PUNCT
ejpam-6331	176	24	is	be	AUX
ejpam-6331	176	25	proved	prove	VERB
ejpam-6331	176	26	.	.	PUNCT
ejpam-6331	177	1	(	(	PUNCT
ejpam-6331	177	2	2	2	X
ejpam-6331	177	3	)	)	PUNCT
ejpam-6331	177	4	⇒	⇒	NOUN
ejpam-6331	177	5	(	(	PUNCT
ejpam-6331	177	6	3	3	X
ejpam-6331	177	7	)	)	PUNCT
ejpam-6331	177	8	assume	assume	VERB
ejpam-6331	177	9	that	that	SCONJ
ejpam-6331	177	10	(	(	PUNCT
ejpam-6331	177	11	2	2	X
ejpam-6331	177	12	)	)	PUNCT
ejpam-6331	177	13	is	be	AUX
ejpam-6331	177	14	satisfied	satisfied	ADJ
ejpam-6331	177	15	.	.	PUNCT
ejpam-6331	178	1	by	by	ADP
ejpam-6331	178	2	using	use	VERB
ejpam-6331	178	3	(	(	PUNCT
ejpam-6331	178	4	⌜	⌜	PROPN
ejpam-6331	178	5	ϱ̃	ϱ̃	PROPN
ejpam-6331	178	6	⌝	⌝	PROPN
ejpam-6331	178	7	∗	∗	NOUN
ejpam-6331	178	8	⌜	⌜	PROPN
ejpam-6331	178	9	ϑ̃	ϑ̃	PROPN
ejpam-6331	178	10	⌝	⌝	PROPN
ejpam-6331	178	11	)	)	PUNCT
ejpam-6331	178	12	∗	∗	NOUN
ejpam-6331	178	13	⌜	⌜	NUM
ejpam-6331	178	14	κ̃	κ̃	PROPN
ejpam-6331	178	15	⌝	⌝	PROPN
ejpam-6331	178	16	=	=	SYM
ejpam-6331	178	17	(	(	PUNCT
ejpam-6331	178	18	⌜	⌜	NOUN
ejpam-6331	178	19	ϱ̃	ϱ̃	PROPN
ejpam-6331	178	20	⌝	⌝	PROPN
ejpam-6331	178	21	∗	∗	NOUN
ejpam-6331	178	22	⌜	⌜	PROPN
ejpam-6331	178	23	κ̃	κ̃	PROPN
ejpam-6331	178	24	⌝	⌝	PROPN
ejpam-6331	178	25	)	)	PUNCT
ejpam-6331	178	26	∗	∗	NOUN
ejpam-6331	178	27	⌜	⌜	PROPN
ejpam-6331	178	28	ϑ̃	ϑ̃	PROPN
ejpam-6331	178	29	⌝	⌝	PROPN
ejpam-6331	178	30	and	and	CCONJ
ejpam-6331	178	31	bci-1	bci-1	PRON
ejpam-6331	178	32	,	,	PUNCT
ejpam-6331	178	33	bci-3	bci-3	X
ejpam-6331	178	34	,	,	PUNCT
ejpam-6331	178	35	we	we	PRON
ejpam-6331	178	36	have	have	VERB
ejpam-6331	178	37	(	(	PUNCT
ejpam-6331	178	38	(	(	PUNCT
ejpam-6331	178	39	⌜	⌜	NOUN
ejpam-6331	179	1	ϱ̃	ϱ̃	PROPN
ejpam-6331	179	2	⌝	⌝	PROPN
ejpam-6331	179	3	∗	∗	NOUN
ejpam-6331	179	4	⌜	⌜	PROPN
ejpam-6331	179	5	ϑ̃	ϑ̃	PROPN
ejpam-6331	179	6	⌝	⌝	PROPN
ejpam-6331	179	7	)	)	PUNCT
ejpam-6331	179	8	∗	∗	NOUN
ejpam-6331	179	9	(	(	PUNCT
ejpam-6331	179	10	0	0	NUM
ejpam-6331	179	11	∗	∗	NOUN
ejpam-6331	179	12	⌜	⌜	PROPN
ejpam-6331	179	13	κ̃	κ̃	PROPN
ejpam-6331	179	14	⌝	⌝	PROPN
ejpam-6331	179	15	)	)	PUNCT
ejpam-6331	179	16	)	)	PUNCT
ejpam-6331	179	17	∗	∗	NOUN
ejpam-6331	179	18	(	(	PUNCT
ejpam-6331	179	19	⌜	⌜	NOUN
ejpam-6331	179	20	ϱ̃	ϱ̃	PROPN
ejpam-6331	179	21	⌝	⌝	PROPN
ejpam-6331	179	22	∗	∗	NOUN
ejpam-6331	179	23	(	(	PUNCT
ejpam-6331	179	24	⌜	⌜	PROPN
ejpam-6331	179	25	ϑ̃	ϑ̃	PROPN
ejpam-6331	179	26	⌝	⌝	PROPN
ejpam-6331	179	27	∗	∗	NOUN
ejpam-6331	179	28	⌜	⌜	PROPN
ejpam-6331	179	29	κ̃	κ̃	PROPN
ejpam-6331	179	30	⌝	⌝	PROPN
ejpam-6331	179	31	)	)	PUNCT
ejpam-6331	179	32	)	)	PUNCT
ejpam-6331	180	1	=	=	PUNCT
ejpam-6331	180	2	(	(	PUNCT
ejpam-6331	180	3	(	(	PUNCT
ejpam-6331	180	4	⌜	⌜	NOUN
ejpam-6331	180	5	ϱ̃	ϱ̃	PROPN
ejpam-6331	180	6	⌝	⌝	PROPN
ejpam-6331	180	7	∗	∗	NOUN
ejpam-6331	180	8	⌜	⌜	PROPN
ejpam-6331	180	9	ϑ̃	ϑ̃	PROPN
ejpam-6331	180	10	⌝	⌝	PROPN
ejpam-6331	180	11	)	)	PUNCT
ejpam-6331	180	12	∗	∗	NOUN
ejpam-6331	180	13	(	(	PUNCT
ejpam-6331	180	14	⌜	⌜	NOUN
ejpam-6331	180	15	ϱ̃	ϱ̃	PROPN
ejpam-6331	180	16	⌝	⌝	PROPN
ejpam-6331	180	17	∗	∗	NOUN
ejpam-6331	180	18	(	(	PUNCT
ejpam-6331	180	19	⌜	⌜	PROPN
ejpam-6331	180	20	ϑ̃	ϑ̃	PROPN
ejpam-6331	180	21	⌝	⌝	PROPN
ejpam-6331	180	22	∗	∗	NOUN
ejpam-6331	180	23	⌜	⌜	PROPN
ejpam-6331	180	24	κ̃	κ̃	PROPN
ejpam-6331	180	25	⌝	⌝	PROPN
ejpam-6331	180	26	)	)	PUNCT
ejpam-6331	180	27	)	)	PUNCT
ejpam-6331	180	28	)	)	PUNCT
ejpam-6331	181	1	∗	∗	NOUN
ejpam-6331	181	2	(	(	PUNCT
ejpam-6331	181	3	0	0	NUM
ejpam-6331	181	4	∗	∗	NOUN
ejpam-6331	181	5	⌜	⌜	PROPN
ejpam-6331	181	6	κ̃	κ̃	PROPN
ejpam-6331	181	7	⌝	⌝	PROPN
ejpam-6331	181	8	)	)	PUNCT
ejpam-6331	181	9	≤	≤	NOUN
ejpam-6331	181	10	(	(	PUNCT
ejpam-6331	181	11	(	(	PUNCT
ejpam-6331	181	12	⌜	⌜	PROPN
ejpam-6331	181	13	ϑ̃	ϑ̃	PROPN
ejpam-6331	181	14	⌝	⌝	PROPN
ejpam-6331	181	15	∗	∗	NOUN
ejpam-6331	181	16	⌜	⌜	PROPN
ejpam-6331	181	17	κ̃	κ̃	PROPN
ejpam-6331	181	18	⌝	⌝	PROPN
ejpam-6331	181	19	)	)	PUNCT
ejpam-6331	181	20	∗	∗	NOUN
ejpam-6331	181	21	⌜	⌜	PROPN
ejpam-6331	181	22	ϑ̃	ϑ̃	PROPN
ejpam-6331	181	23	⌝	⌝	PROPN
ejpam-6331	181	24	)	)	PUNCT
ejpam-6331	181	25	∗	∗	NOUN
ejpam-6331	181	26	(	(	PUNCT
ejpam-6331	181	27	0	0	NUM
ejpam-6331	181	28	∗	∗	NOUN
ejpam-6331	181	29	⌜	⌜	PROPN
ejpam-6331	181	30	κ̃	κ̃	PROPN
ejpam-6331	181	31	⌝	⌝	PROPN
ejpam-6331	181	32	)	)	PUNCT
ejpam-6331	181	33	≤	≤	NOUN
ejpam-6331	181	34	(	(	PUNCT
ejpam-6331	181	35	(	(	PUNCT
ejpam-6331	181	36	⌜	⌜	PROPN
ejpam-6331	181	37	ϑ̃	ϑ̃	PROPN
ejpam-6331	181	38	⌝	⌝	PROPN
ejpam-6331	181	39	∗	∗	PROPN
ejpam-6331	181	40	⌜	⌜	PROPN
ejpam-6331	181	41	ϑ̃	ϑ̃	PROPN
ejpam-6331	181	42	⌝	⌝	PROPN
ejpam-6331	181	43	)	)	PUNCT
ejpam-6331	181	44	∗	∗	NOUN
ejpam-6331	181	45	⌜	⌜	PROPN
ejpam-6331	181	46	κ̃	κ̃	PROPN
ejpam-6331	181	47	⌝	⌝	PROPN
ejpam-6331	181	48	)	)	PUNCT
ejpam-6331	181	49	∗	∗	NOUN
ejpam-6331	181	50	(	(	PUNCT
ejpam-6331	181	51	0	0	NUM
ejpam-6331	181	52	∗	∗	NOUN
ejpam-6331	181	53	⌜	⌜	PROPN
ejpam-6331	181	54	κ̃	κ̃	PROPN
ejpam-6331	181	55	⌝	⌝	PROPN
ejpam-6331	181	56	)	)	PUNCT
ejpam-6331	181	57	≤	≤	NOUN
ejpam-6331	181	58	(	(	PUNCT
ejpam-6331	181	59	0	0	NUM
ejpam-6331	181	60	∗	∗	NOUN
ejpam-6331	181	61	⌜	⌜	PROPN
ejpam-6331	181	62	κ̃	κ̃	PROPN
ejpam-6331	181	63	⌝	⌝	PROPN
ejpam-6331	181	64	)	)	PUNCT
ejpam-6331	181	65	∗	∗	NOUN
ejpam-6331	181	66	(	(	PUNCT
ejpam-6331	181	67	0	0	NUM
ejpam-6331	181	68	∗	∗	NOUN
ejpam-6331	181	69	⌜	⌜	PROPN
ejpam-6331	181	70	κ̃	κ̃	PROPN
ejpam-6331	181	71	⌝	⌝	PROPN
ejpam-6331	181	72	)	)	PUNCT
ejpam-6331	181	73	≤	≤	NOUN
ejpam-6331	181	74	0	0	NUM
ejpam-6331	181	75	.	.	PUNCT
ejpam-6331	182	1	hence	hence	ADV
ejpam-6331	182	2	,	,	PUNCT
ejpam-6331	182	3	(	(	PUNCT
ejpam-6331	182	4	⌜	⌜	NOUN
ejpam-6331	182	5	ϱ̃	ϱ̃	PROPN
ejpam-6331	182	6	⌝	⌝	PROPN
ejpam-6331	182	7	∗	∗	NOUN
ejpam-6331	182	8	⌜	⌜	PROPN
ejpam-6331	182	9	ϑ̃	ϑ̃	PROPN
ejpam-6331	182	10	⌝	⌝	PROPN
ejpam-6331	182	11	)	)	PUNCT
ejpam-6331	182	12	∗	∗	NOUN
ejpam-6331	182	13	(	(	PUNCT
ejpam-6331	182	14	0	0	NUM
ejpam-6331	182	15	∗	∗	NOUN
ejpam-6331	182	16	⌜	⌜	PROPN
ejpam-6331	182	17	κ̃	κ̃	PROPN
ejpam-6331	182	18	⌝	⌝	PROPN
ejpam-6331	182	19	)	)	PUNCT
ejpam-6331	182	20	≤	≤	PUNCT
ejpam-6331	183	1	⌜	⌜	PUNCT
ejpam-6331	183	2	ϱ̃	ϱ̃	PROPN
ejpam-6331	183	3	⌝	⌝	PROPN
ejpam-6331	183	4	∗	∗	NOUN
ejpam-6331	183	5	(	(	PUNCT
ejpam-6331	183	6	⌜	⌜	PROPN
ejpam-6331	183	7	ϑ̃	ϑ̃	PROPN
ejpam-6331	183	8	⌝	⌝	PROPN
ejpam-6331	183	9	∗	∗	NOUN
ejpam-6331	183	10	⌜	⌜	PROPN
ejpam-6331	183	11	κ̃	κ̃	PROPN
ejpam-6331	183	12	⌝	⌝	PROPN
ejpam-6331	183	13	)	)	PUNCT
ejpam-6331	183	14	.	.	PUNCT
ejpam-6331	184	1	by	by	ADP
ejpam-6331	184	2	lemma	lemma	PROPN
ejpam-6331	184	3	1	1	NUM
ejpam-6331	184	4	,	,	PUNCT
ejpam-6331	184	5	we	we	PRON
ejpam-6331	184	6	get	get	VERB
ejpam-6331	184	7	∅̃c((	∅̃c((	PROPN
ejpam-6331	184	8	⌜	⌜	NOUN
ejpam-6331	184	9	ϱ̃	ϱ̃	PROPN
ejpam-6331	184	10	⌝	⌝	PROPN
ejpam-6331	184	11	∗	∗	NOUN
ejpam-6331	184	12	⌜	⌜	PROPN
ejpam-6331	184	13	ϑ̃	ϑ̃	PROPN
ejpam-6331	184	14	⌝	⌝	PROPN
ejpam-6331	184	15	)	)	PUNCT
ejpam-6331	184	16	∗	∗	NOUN
ejpam-6331	184	17	⌜	⌜	PROPN
ejpam-6331	184	18	κ̃	κ̃	PROPN
ejpam-6331	184	19	⌝	⌝	PROPN
ejpam-6331	184	20	)eiω̃c((	)eiω̃c((	PROPN
ejpam-6331	184	21	⌜	⌜	PROPN
ejpam-6331	184	22	ϱ̃	ϱ̃	PROPN
ejpam-6331	184	23	⌝	⌝	PROPN
ejpam-6331	184	24	∗	∗	NOUN
ejpam-6331	184	25	⌜	⌜	PROPN
ejpam-6331	184	26	ϑ̃	ϑ̃	PROPN
ejpam-6331	184	27	⌝	⌝	PROPN
ejpam-6331	184	28	)∗	)∗	PROPN
ejpam-6331	184	29	⌜	⌜	PROPN
ejpam-6331	184	30	κ̃	κ̃	PROPN
ejpam-6331	184	31	⌝	⌝	PROPN
ejpam-6331	184	32	)	)	PUNCT
ejpam-6331	184	33	≥	≥	NOUN
ejpam-6331	184	34	∅̃c(	∅̃c(	NOUN
ejpam-6331	184	35	⌜	⌜	NOUN
ejpam-6331	184	36	ϱ̃	ϱ̃	PROPN
ejpam-6331	184	37	⌝	⌝	PROPN
ejpam-6331	184	38	∗	∗	NOUN
ejpam-6331	184	39	⌜	⌜	PROPN
ejpam-6331	184	40	ϑ̃	ϑ̃	PROPN
ejpam-6331	184	41	⌝	⌝	PROPN
ejpam-6331	184	42	)	)	PUNCT
ejpam-6331	184	43	∗	∗	NOUN
ejpam-6331	184	44	⌜	⌜	PROPN
ejpam-6331	184	45	κ̃	κ̃	PROPN
ejpam-6331	184	46	⌝	⌝	PROPN
ejpam-6331	184	47	))eiω̃c(	))eiω̃c(	PROPN
ejpam-6331	184	48	⌜	⌜	PROPN
ejpam-6331	184	49	ϱ̃	ϱ̃	PROPN
ejpam-6331	184	50	⌝	⌝	PROPN
ejpam-6331	184	51	∗	∗	NOUN
ejpam-6331	184	52	⌜	⌜	PROPN
ejpam-6331	184	53	ϑ̃	ϑ̃	PROPN
ejpam-6331	184	54	⌝	⌝	PROPN
ejpam-6331	184	55	)∗	)∗	PROPN
ejpam-6331	184	56	⌜	⌜	PROPN
ejpam-6331	184	57	κ̃	κ̃	PROPN
ejpam-6331	184	58	⌝	⌝	PROPN
ejpam-6331	184	59	)	)	PUNCT
ejpam-6331	184	60	)	)	PUNCT
ejpam-6331	184	61	and	and	CCONJ
ejpam-6331	184	62	φ̃c((	φ̃c((	ADP
ejpam-6331	184	63	⌜	⌜	NOUN
ejpam-6331	184	64	ϱ̃	ϱ̃	PROPN
ejpam-6331	184	65	⌝	⌝	PROPN
ejpam-6331	184	66	∗	∗	NOUN
ejpam-6331	184	67	⌜	⌜	PROPN
ejpam-6331	184	68	ϑ̃	ϑ̃	PROPN
ejpam-6331	184	69	⌝	⌝	PROPN
ejpam-6331	184	70	)	)	PUNCT
ejpam-6331	184	71	∗	∗	NOUN
ejpam-6331	184	72	⌜	⌜	PROPN
ejpam-6331	184	73	κ̃	κ̃	PROPN
ejpam-6331	184	74	⌝	⌝	PROPN
ejpam-6331	184	75	)eiθ̃c((	)eiθ̃c((	NOUN
ejpam-6331	184	76	⌜	⌜	PROPN
ejpam-6331	184	77	ϱ̃	ϱ̃	PROPN
ejpam-6331	184	78	⌝	⌝	PROPN
ejpam-6331	184	79	∗	∗	NOUN
ejpam-6331	184	80	⌜	⌜	PROPN
ejpam-6331	184	81	ϑ̃	ϑ̃	PROPN
ejpam-6331	184	82	⌝	⌝	PROPN
ejpam-6331	184	83	)∗	)∗	PROPN
ejpam-6331	184	84	⌜	⌜	PROPN
ejpam-6331	184	85	κ̃	κ̃	PROPN
ejpam-6331	184	86	⌝	⌝	PROPN
ejpam-6331	184	87	)	)	PUNCT
ejpam-6331	184	88	≤	≤	NOUN
ejpam-6331	184	89	φ̃c(	φ̃c(	NOUN
ejpam-6331	184	90	⌜	⌜	NOUN
ejpam-6331	185	1	ϱ̃	ϱ̃	PROPN
ejpam-6331	185	2	⌝	⌝	PROPN
ejpam-6331	185	3	∗	∗	NOUN
ejpam-6331	185	4	⌜	⌜	PROPN
ejpam-6331	185	5	ϑ̃	ϑ̃	PROPN
ejpam-6331	185	6	⌝	⌝	PROPN
ejpam-6331	185	7	)	)	PUNCT
ejpam-6331	185	8	∗	∗	NOUN
ejpam-6331	185	9	⌜	⌜	PROPN
ejpam-6331	185	10	κ̃	κ̃	PROPN
ejpam-6331	185	11	⌝	⌝	PROPN
ejpam-6331	185	12	))eiθ̃c(	))eiθ̃c(	DET
ejpam-6331	185	13	⌜	⌜	PROPN
ejpam-6331	185	14	ϱ̃	ϱ̃	PROPN
ejpam-6331	185	15	⌝	⌝	PROPN
ejpam-6331	185	16	∗	∗	NOUN
ejpam-6331	185	17	⌜	⌜	PROPN
ejpam-6331	185	18	ϑ̃	ϑ̃	PROPN
ejpam-6331	185	19	⌝	⌝	PROPN
ejpam-6331	185	20	)∗	)∗	PROPN
ejpam-6331	185	21	⌜	⌜	PROPN
ejpam-6331	185	22	κ̃	κ̃	PROPN
ejpam-6331	185	23	⌝	⌝	PROPN
ejpam-6331	185	24	)	)	PUNCT
ejpam-6331	185	25	)	)	PUNCT
ejpam-6331	185	26	.	.	PUNCT
ejpam-6331	186	1	hence	hence	ADV
ejpam-6331	186	2	,	,	PUNCT
ejpam-6331	186	3	(	(	PUNCT
ejpam-6331	186	4	3	3	X
ejpam-6331	186	5	)	)	PUNCT
ejpam-6331	186	6	is	be	AUX
ejpam-6331	186	7	proved	prove	VERB
ejpam-6331	186	8	.	.	PUNCT
ejpam-6331	187	1	(	(	PUNCT
ejpam-6331	187	2	3	3	X
ejpam-6331	187	3	)	)	PUNCT
ejpam-6331	187	4	⇒	⇒	NOUN
ejpam-6331	187	5	(	(	PUNCT
ejpam-6331	187	6	1	1	X
ejpam-6331	187	7	)	)	PUNCT
ejpam-6331	187	8	assume	assume	VERB
ejpam-6331	187	9	that	that	SCONJ
ejpam-6331	187	10	(	(	PUNCT
ejpam-6331	187	11	3	3	X
ejpam-6331	187	12	)	)	PUNCT
ejpam-6331	187	13	is	be	AUX
ejpam-6331	187	14	satisfied	satisfied	ADJ
ejpam-6331	187	15	.	.	PUNCT
ejpam-6331	188	1	by	by	ADP
ejpam-6331	188	2	using	use	VERB
ejpam-6331	188	3	cifi-2	cifi-2	NUM
ejpam-6331	188	4	and	and	CCONJ
ejpam-6331	188	5	cifi-3	cifi-3	NOUN
ejpam-6331	188	6	in	in	ADP
ejpam-6331	188	7	definition	definition	NOUN
ejpam-6331	188	8	6	6	NUM
ejpam-6331	188	9	,	,	PUNCT
ejpam-6331	188	10	(	(	PUNCT
ejpam-6331	188	11	⌜	⌜	NOUN
ejpam-6331	188	12	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	13	⌝	⌝	PROPN
ejpam-6331	188	14	∗	∗	NOUN
ejpam-6331	188	15	⌜	⌜	PROPN
ejpam-6331	188	16	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	17	⌝	⌝	PROPN
ejpam-6331	188	18	)	)	PUNCT
ejpam-6331	188	19	∗	∗	NOUN
ejpam-6331	188	20	⌜	⌜	NUM
ejpam-6331	188	21	κ̃	κ̃	PROPN
ejpam-6331	188	22	⌝	⌝	PROPN
ejpam-6331	188	23	=	=	SYM
ejpam-6331	188	24	(	(	PUNCT
ejpam-6331	188	25	⌜	⌜	NOUN
ejpam-6331	188	26	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	27	⌝	⌝	PROPN
ejpam-6331	188	28	∗	∗	NOUN
ejpam-6331	188	29	⌜	⌜	PROPN
ejpam-6331	188	30	κ̃	κ̃	PROPN
ejpam-6331	188	31	⌝	⌝	PROPN
ejpam-6331	188	32	)	)	PUNCT
ejpam-6331	188	33	∗	∗	NOUN
ejpam-6331	188	34	⌜	⌜	PROPN
ejpam-6331	188	35	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	36	⌝	⌝	PROPN
ejpam-6331	188	37	and	and	CCONJ
ejpam-6331	188	38	(	(	PUNCT
ejpam-6331	188	39	3	3	NUM
ejpam-6331	188	40	)	)	PUNCT
ejpam-6331	188	41	,	,	PUNCT
ejpam-6331	188	42	we	we	PRON
ejpam-6331	188	43	have	have	VERB
ejpam-6331	188	44	∅̃c(	∅̃c(	NOUN
ejpam-6331	188	45	⌜	⌜	NOUN
ejpam-6331	188	46	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	47	⌝	⌝	PROPN
ejpam-6331	188	48	∗	∗	NOUN
ejpam-6331	188	49	⌜	⌜	PROPN
ejpam-6331	188	50	κ̃	κ̃	PROPN
ejpam-6331	188	51	⌝	⌝	PROPN
ejpam-6331	188	52	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	188	53	⌜	⌜	PROPN
ejpam-6331	188	54	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	55	⌝	⌝	PROPN
ejpam-6331	188	56	∗	∗	NOUN
ejpam-6331	188	57	⌜	⌜	PROPN
ejpam-6331	188	58	κ̃	κ̃	PROPN
ejpam-6331	188	59	⌝	⌝	PROPN
ejpam-6331	188	60	)	)	PUNCT
ejpam-6331	188	61	≥	≥	NOUN
ejpam-6331	188	62	min{∅̃c((	min{∅̃c((	PROPN
ejpam-6331	188	63	⌜	⌜	PROPN
ejpam-6331	188	64	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	65	⌝	⌝	PROPN
ejpam-6331	188	66	∗	∗	NOUN
ejpam-6331	188	67	⌜	⌜	PROPN
ejpam-6331	188	68	κ̃	κ̃	PROPN
ejpam-6331	188	69	⌝	⌝	PROPN
ejpam-6331	188	70	)	)	PUNCT
ejpam-6331	188	71	∗	∗	NOUN
ejpam-6331	188	72	⌜	⌜	PROPN
ejpam-6331	188	73	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	74	⌝	⌝	PROPN
ejpam-6331	188	75	)eiω̃c((	)eiω̃c((	PROPN
ejpam-6331	188	76	⌜	⌜	PROPN
ejpam-6331	188	77	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	78	⌝	⌝	PROPN
ejpam-6331	188	79	∗	∗	NOUN
ejpam-6331	188	80	⌜	⌜	PROPN
ejpam-6331	188	81	κ̃	κ̃	PROPN
ejpam-6331	188	82	⌝	⌝	PROPN
ejpam-6331	188	83	)∗	)∗	PROPN
ejpam-6331	188	84	⌜	⌜	PROPN
ejpam-6331	188	85	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	86	⌝	⌝	PROPN
ejpam-6331	188	87	)	)	PUNCT
ejpam-6331	188	88	,	,	PUNCT
ejpam-6331	188	89	∅̃c(	∅̃c(	NOUN
ejpam-6331	188	90	⌜	⌜	SYM
ejpam-6331	188	91	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	92	⌝	⌝	PROPN
ejpam-6331	188	93	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	188	94	⌜	⌜	PROPN
ejpam-6331	188	95	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	96	⌝	⌝	PROPN
ejpam-6331	188	97	)	)	PUNCT
ejpam-6331	188	98	}	}	PUNCT
ejpam-6331	188	99	≥	≥	PROPN
ejpam-6331	188	100	min{∅̃c((	min{∅̃c((	PROPN
ejpam-6331	188	101	⌜	⌜	PROPN
ejpam-6331	188	102	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	103	⌝	⌝	PROPN
ejpam-6331	188	104	∗	∗	NOUN
ejpam-6331	188	105	⌜	⌜	PROPN
ejpam-6331	188	106	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	107	⌝	⌝	PROPN
ejpam-6331	188	108	)	)	PUNCT
ejpam-6331	188	109	∗	∗	NOUN
ejpam-6331	188	110	⌜	⌜	PROPN
ejpam-6331	188	111	κ̃	κ̃	PROPN
ejpam-6331	188	112	⌝	⌝	PROPN
ejpam-6331	188	113	)eiω̃c((	)eiω̃c((	PROPN
ejpam-6331	188	114	⌜	⌜	PROPN
ejpam-6331	188	115	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	116	⌝	⌝	PROPN
ejpam-6331	188	117	∗	∗	NOUN
ejpam-6331	188	118	⌜	⌜	PROPN
ejpam-6331	188	119	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	120	⌝	⌝	PROPN
ejpam-6331	188	121	)∗	)∗	PROPN
ejpam-6331	188	122	⌜	⌜	PROPN
ejpam-6331	188	123	κ̃	κ̃	PROPN
ejpam-6331	188	124	⌝	⌝	PROPN
ejpam-6331	188	125	)	)	PUNCT
ejpam-6331	188	126	,	,	PUNCT
ejpam-6331	188	127	∅̃c(	∅̃c(	NOUN
ejpam-6331	188	128	⌜	⌜	SYM
ejpam-6331	188	129	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	130	⌝	⌝	PROPN
ejpam-6331	188	131	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	188	132	⌜	⌜	PROPN
ejpam-6331	188	133	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	134	⌝	⌝	PROPN
ejpam-6331	188	135	)	)	PUNCT
ejpam-6331	188	136	}	}	PUNCT
ejpam-6331	188	137	≥	≥	VERB
ejpam-6331	188	138	min{∅̃c(	min{∅̃c(	PRON
ejpam-6331	188	139	⌜	⌜	PROPN
ejpam-6331	188	140	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	141	⌝	⌝	PROPN
ejpam-6331	188	142	∗	∗	NOUN
ejpam-6331	188	143	(	(	PUNCT
ejpam-6331	188	144	⌜	⌜	PROPN
ejpam-6331	188	145	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	146	⌝	⌝	PROPN
ejpam-6331	188	147	∗	∗	NOUN
ejpam-6331	188	148	⌜	⌜	PROPN
ejpam-6331	188	149	κ̃	κ̃	PROPN
ejpam-6331	188	150	⌝	⌝	PROPN
ejpam-6331	188	151	))eiω̃c(	))eiω̃c(	PROPN
ejpam-6331	188	152	⌜	⌜	PROPN
ejpam-6331	188	153	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	154	⌝	⌝	PROPN
ejpam-6331	188	155	∗(	∗(	NOUN
ejpam-6331	188	156	⌜	⌜	PROPN
ejpam-6331	188	157	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	158	⌝	⌝	PROPN
ejpam-6331	188	159	∗	∗	NOUN
ejpam-6331	188	160	⌜	⌜	PROPN
ejpam-6331	188	161	κ̃	κ̃	PROPN
ejpam-6331	188	162	⌝	⌝	PROPN
ejpam-6331	188	163	)	)	PUNCT
ejpam-6331	188	164	)	)	PUNCT
ejpam-6331	188	165	,	,	PUNCT
ejpam-6331	188	166	∅̃c(	∅̃c(	NOUN
ejpam-6331	188	167	⌜	⌜	SYM
ejpam-6331	188	168	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	169	⌝	⌝	PROPN
ejpam-6331	188	170	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	188	171	⌜	⌜	PROPN
ejpam-6331	188	172	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	173	⌝	⌝	PROPN
ejpam-6331	188	174	)	)	PUNCT
ejpam-6331	188	175	}	}	PUNCT
ejpam-6331	188	176	and	and	CCONJ
ejpam-6331	188	177	φ̃c(	φ̃c(	PROPN
ejpam-6331	188	178	⌜	⌜	NOUN
ejpam-6331	188	179	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	180	⌝	⌝	PROPN
ejpam-6331	188	181	∗	∗	NOUN
ejpam-6331	188	182	⌜	⌜	PROPN
ejpam-6331	188	183	κ̃	κ̃	PROPN
ejpam-6331	188	184	⌝	⌝	PROPN
ejpam-6331	188	185	)eiθ̃c(	)eiθ̃c(	ADJ
ejpam-6331	188	186	⌜	⌜	PROPN
ejpam-6331	188	187	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	188	⌝	⌝	PROPN
ejpam-6331	188	189	∗	∗	NOUN
ejpam-6331	188	190	⌜	⌜	PROPN
ejpam-6331	188	191	κ̃	κ̃	PROPN
ejpam-6331	188	192	⌝	⌝	PROPN
ejpam-6331	188	193	)	)	PUNCT
ejpam-6331	188	194	≤	≤	PUNCT
ejpam-6331	188	195	max{φ̃c((	max{φ̃c((	PROPN
ejpam-6331	188	196	⌜	⌜	PROPN
ejpam-6331	188	197	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	198	⌝	⌝	PROPN
ejpam-6331	188	199	∗	∗	NOUN
ejpam-6331	188	200	⌜	⌜	PROPN
ejpam-6331	188	201	κ̃	κ̃	PROPN
ejpam-6331	188	202	⌝	⌝	PROPN
ejpam-6331	188	203	)	)	PUNCT
ejpam-6331	188	204	∗	∗	NOUN
ejpam-6331	188	205	⌜	⌜	PROPN
ejpam-6331	188	206	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	207	⌝	⌝	PROPN
ejpam-6331	188	208	)eiθ̃c((	)eiθ̃c((	PROPN
ejpam-6331	188	209	⌜	⌜	PROPN
ejpam-6331	188	210	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	211	⌝	⌝	PROPN
ejpam-6331	188	212	∗	∗	NOUN
ejpam-6331	188	213	⌜	⌜	PROPN
ejpam-6331	188	214	κ̃	κ̃	PROPN
ejpam-6331	188	215	⌝	⌝	PROPN
ejpam-6331	188	216	)∗	)∗	PROPN
ejpam-6331	188	217	⌜	⌜	PROPN
ejpam-6331	188	218	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	219	⌝	⌝	PROPN
ejpam-6331	188	220	)	)	PUNCT
ejpam-6331	188	221	,	,	PUNCT
ejpam-6331	188	222	φ̃c(m)eiθ̃c(m	φ̃c(m)eiθ̃c(m	PROPN
ejpam-6331	188	223	)	)	PUNCT
ejpam-6331	188	224	}	}	PUNCT
ejpam-6331	188	225	≤	≤	NUM
ejpam-6331	188	226	max{φ̃c((	max{φ̃c((	PROPN
ejpam-6331	188	227	⌜	⌜	PROPN
ejpam-6331	188	228	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	229	⌝	⌝	PROPN
ejpam-6331	188	230	∗	∗	NOUN
ejpam-6331	188	231	⌜	⌜	PROPN
ejpam-6331	188	232	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	233	⌝	⌝	PROPN
ejpam-6331	188	234	)	)	PUNCT
ejpam-6331	188	235	∗	∗	NOUN
ejpam-6331	188	236	⌜	⌜	PROPN
ejpam-6331	188	237	κ̃	κ̃	PROPN
ejpam-6331	188	238	⌝	⌝	PROPN
ejpam-6331	188	239	)eiθ̃c((	)eiθ̃c((	NOUN
ejpam-6331	188	240	⌜	⌜	PROPN
ejpam-6331	188	241	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	242	⌝	⌝	PROPN
ejpam-6331	188	243	∗	∗	NOUN
ejpam-6331	188	244	⌜	⌜	PROPN
ejpam-6331	188	245	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	246	⌝	⌝	PROPN
ejpam-6331	188	247	)∗	)∗	PROPN
ejpam-6331	188	248	⌜	⌜	PROPN
ejpam-6331	188	249	κ̃	κ̃	PROPN
ejpam-6331	188	250	⌝	⌝	PROPN
ejpam-6331	188	251	)	)	PUNCT
ejpam-6331	188	252	,	,	PUNCT
ejpam-6331	188	253	φ̃c(	φ̃c(	PROPN
ejpam-6331	188	254	⌜	⌜	PROPN
ejpam-6331	188	255	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	256	⌝	⌝	PROPN
ejpam-6331	188	257	)e	)e	NOUN
ejpam-6331	188	258	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	188	259	⌜	⌜	PROPN
ejpam-6331	188	260	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	261	⌝	⌝	PROPN
ejpam-6331	188	262	)	)	PUNCT
ejpam-6331	188	263	}	}	PUNCT
ejpam-6331	188	264	≤	≤	NUM
ejpam-6331	188	265	max{φ̃c(	max{φ̃c(	PUNCT
ejpam-6331	188	266	⌜	⌜	NOUN
ejpam-6331	188	267	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	268	⌝	⌝	PROPN
ejpam-6331	188	269	∗	∗	NOUN
ejpam-6331	188	270	(	(	PUNCT
ejpam-6331	188	271	⌜	⌜	PROPN
ejpam-6331	188	272	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	273	⌝	⌝	PROPN
ejpam-6331	188	274	∗	∗	NOUN
ejpam-6331	188	275	⌜	⌜	PROPN
ejpam-6331	188	276	κ̃	κ̃	PROPN
ejpam-6331	188	277	⌝	⌝	PROPN
ejpam-6331	188	278	))eiθ̃c(	))eiθ̃c(	DET
ejpam-6331	188	279	⌜	⌜	PROPN
ejpam-6331	188	280	ϱ̃	ϱ̃	PROPN
ejpam-6331	188	281	⌝	⌝	PROPN
ejpam-6331	188	282	∗(	∗(	NOUN
ejpam-6331	188	283	⌜	⌜	PROPN
ejpam-6331	188	284	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	285	⌝	⌝	PROPN
ejpam-6331	188	286	∗	∗	NOUN
ejpam-6331	188	287	⌜	⌜	PROPN
ejpam-6331	188	288	κ̃	κ̃	PROPN
ejpam-6331	188	289	⌝	⌝	PROPN
ejpam-6331	188	290	)	)	PUNCT
ejpam-6331	188	291	)	)	PUNCT
ejpam-6331	188	292	,	,	PUNCT
ejpam-6331	188	293	φ̃c(	φ̃c(	PROPN
ejpam-6331	188	294	⌜	⌜	PROPN
ejpam-6331	188	295	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	296	⌝	⌝	PROPN
ejpam-6331	188	297	)e	)e	NOUN
ejpam-6331	188	298	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	188	299	⌜	⌜	PROPN
ejpam-6331	188	300	ϑ̃	ϑ̃	PROPN
ejpam-6331	188	301	⌝	⌝	PROPN
ejpam-6331	188	302	)	)	PUNCT
ejpam-6331	188	303	}	}	PUNCT
ejpam-6331	188	304	.	.	PUNCT
ejpam-6331	189	1	thus	thus	ADV
ejpam-6331	189	2	,	,	PUNCT
ejpam-6331	189	3	cifqai-1	cifqai-1	NUM
ejpam-6331	189	4	and	and	CCONJ
ejpam-6331	189	5	cifqai-2	cifqai-2	NUM
ejpam-6331	189	6	are	be	AUX
ejpam-6331	189	7	satisfied	satisfied	ADJ
ejpam-6331	189	8	.	.	PUNCT
ejpam-6331	190	1	hence	hence	ADV
ejpam-6331	190	2	,	,	PUNCT
ejpam-6331	190	3	c	c	X
ejpam-6331	190	4	=	=	SYM
ejpam-6331	190	5	(	(	PUNCT
ejpam-6331	190	6	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	190	7	,	,	PUNCT
ejpam-6331	190	8	φ̃ce	φ̃ce	PROPN
ejpam-6331	190	9	iθ̃c	iθ̃c	PROPN
ejpam-6331	190	10	)	)	PUNCT
ejpam-6331	190	11	is	be	AUX
ejpam-6331	190	12	a	a	DET
ejpam-6331	190	13	cifqaideal	cifqaideal	NOUN
ejpam-6331	190	14	.	.	PUNCT
ejpam-6331	191	1	t.	t.	PROPN
ejpam-6331	191	2	ramesh	ramesh	PROPN
ejpam-6331	191	3	,	,	PUNCT
ejpam-6331	191	4	m.	m.	NOUN
ejpam-6331	191	5	balamurugan	balamurugan	PROPN
ejpam-6331	191	6	,	,	PUNCT
ejpam-6331	191	7	a.	a.	NOUN
ejpam-6331	191	8	iampan	iampan	PROPN
ejpam-6331	191	9	/	/	SYM
ejpam-6331	191	10	eur	eur	PROPN
ejpam-6331	191	11	.	.	PUNCT
ejpam-6331	192	1	j.	j.	PROPN
ejpam-6331	192	2	pure	pure	PROPN
ejpam-6331	192	3	appl	appl	PROPN
ejpam-6331	192	4	.	.	PROPN
ejpam-6331	192	5	math	math	PROPN
ejpam-6331	192	6	,	,	PUNCT
ejpam-6331	192	7	18	18	NUM
ejpam-6331	192	8	(	(	PUNCT
ejpam-6331	192	9	3	3	NUM
ejpam-6331	192	10	)	)	PUNCT
ejpam-6331	192	11	(	(	PUNCT
ejpam-6331	192	12	2025	2025	NUM
ejpam-6331	192	13	)	)	PUNCT
ejpam-6331	192	14	,	,	PUNCT
ejpam-6331	192	15	6331	6331	NUM
ejpam-6331	192	16	11	11	NUM
ejpam-6331	192	17	of	of	ADP
ejpam-6331	192	18	14	14	NUM
ejpam-6331	192	19	4	4	NUM
ejpam-6331	192	20	.	.	PUNCT
ejpam-6331	193	1	complex	complex	ADJ
ejpam-6331	193	2	intuitionistic	intuitionistic	ADJ
ejpam-6331	193	3	fuzzy	fuzzy	ADJ
ejpam-6331	193	4	b	b	NOUN
ejpam-6331	193	5	-	-	PUNCT
ejpam-6331	193	6	ideals	ideal	NOUN
ejpam-6331	193	7	this	this	DET
ejpam-6331	193	8	section	section	NOUN
ejpam-6331	193	9	focuses	focus	VERB
ejpam-6331	193	10	on	on	ADP
ejpam-6331	193	11	the	the	DET
ejpam-6331	193	12	formulation	formulation	NOUN
ejpam-6331	193	13	and	and	CCONJ
ejpam-6331	193	14	analysis	analysis	NOUN
ejpam-6331	193	15	of	of	ADP
ejpam-6331	193	16	complex	complex	ADJ
ejpam-6331	193	17	intuitionistic	intuitionistic	ADJ
ejpam-6331	193	18	fuzzy	fuzzy	ADJ
ejpam-6331	193	19	b	b	NOUN
ejpam-6331	193	20	-	-	PUNCT
ejpam-6331	193	21	ideals	ideal	NOUN
ejpam-6331	193	22	(	(	PUNCT
ejpam-6331	193	23	cifb	cifb	NOUN
ejpam-6331	193	24	-	-	PUNCT
ejpam-6331	193	25	ideals	ideal	NOUN
ejpam-6331	193	26	)	)	PUNCT
ejpam-6331	193	27	in	in	ADP
ejpam-6331	193	28	bci	bci	NOUN
ejpam-6331	193	29	-	-	PUNCT
ejpam-6331	193	30	algebras	algebras	X
ejpam-6331	193	31	.	.	PUNCT
ejpam-6331	194	1	these	these	DET
ejpam-6331	194	2	ideals	ideal	NOUN
ejpam-6331	194	3	represent	represent	VERB
ejpam-6331	194	4	a	a	DET
ejpam-6331	194	5	refined	refined	ADJ
ejpam-6331	194	6	class	class	NOUN
ejpam-6331	194	7	of	of	ADP
ejpam-6331	194	8	cifideals	cifideal	NOUN
ejpam-6331	194	9	,	,	PUNCT
ejpam-6331	194	10	characterized	characterize	VERB
ejpam-6331	194	11	by	by	ADP
ejpam-6331	194	12	stronger	strong	ADJ
ejpam-6331	194	13	absorption	absorption	NOUN
ejpam-6331	194	14	properties	property	NOUN
ejpam-6331	194	15	under	under	ADP
ejpam-6331	194	16	fuzzy	fuzzy	ADJ
ejpam-6331	194	17	composition	composition	NOUN
ejpam-6331	194	18	.	.	PUNCT
ejpam-6331	195	1	we	we	PRON
ejpam-6331	195	2	define	define	VERB
ejpam-6331	195	3	cifb	cifb	NOUN
ejpam-6331	195	4	-	-	PUNCT
ejpam-6331	195	5	ideals	ideal	NOUN
ejpam-6331	195	6	rigorously	rigorously	ADV
ejpam-6331	195	7	and	and	CCONJ
ejpam-6331	195	8	examine	examine	VERB
ejpam-6331	195	9	their	their	PRON
ejpam-6331	195	10	interrelationships	interrelationship	NOUN
ejpam-6331	195	11	with	with	ADP
ejpam-6331	195	12	previously	previously	ADV
ejpam-6331	195	13	established	establish	VERB
ejpam-6331	195	14	ideal	ideal	ADJ
ejpam-6331	195	15	types	type	NOUN
ejpam-6331	195	16	,	,	PUNCT
ejpam-6331	195	17	highlighting	highlight	VERB
ejpam-6331	195	18	their	their	PRON
ejpam-6331	195	19	role	role	NOUN
ejpam-6331	195	20	in	in	ADP
ejpam-6331	195	21	the	the	DET
ejpam-6331	195	22	broader	broad	ADJ
ejpam-6331	195	23	structure	structure	NOUN
ejpam-6331	195	24	of	of	ADP
ejpam-6331	195	25	fuzzy	fuzzy	ADJ
ejpam-6331	195	26	algebraic	algebraic	ADJ
ejpam-6331	195	27	systems	system	NOUN
ejpam-6331	195	28	.	.	PUNCT
ejpam-6331	196	1	definition	definition	NOUN
ejpam-6331	196	2	8	8	NUM
ejpam-6331	196	3	.	.	PUNCT
ejpam-6331	197	1	a	a	DET
ejpam-6331	197	2	cif	cif	PROPN
ejpam-6331	197	3	-	-	PUNCT
ejpam-6331	197	4	set	set	VERB
ejpam-6331	197	5	c	c	NOUN
ejpam-6331	197	6	=	=	SYM
ejpam-6331	197	7	(	(	PUNCT
ejpam-6331	197	8	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	197	9	,	,	PUNCT
ejpam-6331	197	10	φ̃ce	φ̃ce	PROPN
ejpam-6331	197	11	iθ̃c	iθ̃c	PROPN
ejpam-6331	197	12	)	)	PUNCT
ejpam-6331	197	13	forms	form	VERB
ejpam-6331	197	14	a	a	DET
ejpam-6331	197	15	complex	complex	ADJ
ejpam-6331	197	16	intuitionistic	intuitionistic	ADJ
ejpam-6331	197	17	fuzzy	fuzzy	ADJ
ejpam-6331	197	18	b	b	NOUN
ejpam-6331	197	19	-	-	PUNCT
ejpam-6331	197	20	ideal	ideal	ADJ
ejpam-6331	197	21	(	(	PUNCT
ejpam-6331	197	22	cifb	cifb	NOUN
ejpam-6331	197	23	-	-	PUNCT
ejpam-6331	197	24	ideal	ideal	NOUN
ejpam-6331	197	25	)	)	PUNCT
ejpam-6331	197	26	of	of	ADP
ejpam-6331	197	27	x	x	PRON
ejpam-6331	197	28	if	if	SCONJ
ejpam-6331	197	29	it	it	PRON
ejpam-6331	197	30	satisfies	satisfy	VERB
ejpam-6331	197	31	the	the	DET
ejpam-6331	197	32	following	following	NOUN
ejpam-6331	197	33	:	:	PUNCT
ejpam-6331	197	34	(	(	PUNCT
ejpam-6331	197	35	cifbi-1	cifbi-1	NOUN
ejpam-6331	197	36	)	)	PUNCT
ejpam-6331	197	37	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	NOUN
ejpam-6331	197	38	)	)	PUNCT
ejpam-6331	198	1	≥	≥	NOUN
ejpam-6331	198	2	∅̃c(	∅̃c(	NOUN
ejpam-6331	198	3	⌜	⌜	NOUN
ejpam-6331	198	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	5	⌝	⌝	PROPN
ejpam-6331	198	6	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	198	7	⌜	⌜	PROPN
ejpam-6331	198	8	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	9	⌝	⌝	PROPN
ejpam-6331	198	10	)	)	PUNCT
ejpam-6331	198	11	,	,	PUNCT
ejpam-6331	198	12	φ̃c(0)e	φ̃c(0)e	NOUN
ejpam-6331	198	13	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	198	14	)	)	PUNCT
ejpam-6331	198	15	≤	≤	NOUN
ejpam-6331	198	16	φ̃c(	φ̃c(	NOUN
ejpam-6331	198	17	⌜	⌜	NOUN
ejpam-6331	198	18	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	19	⌝	⌝	PROPN
ejpam-6331	198	20	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	198	21	⌜	⌜	PROPN
ejpam-6331	198	22	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	23	⌝	⌝	PROPN
ejpam-6331	198	24	)	)	PUNCT
ejpam-6331	198	25	,	,	PUNCT
ejpam-6331	198	26	(	(	PUNCT
ejpam-6331	198	27	cifbi-2	cifbi-2	NOUN
ejpam-6331	198	28	)	)	PUNCT
ejpam-6331	198	29	∅̃c(	∅̃c(	NOUN
ejpam-6331	198	30	⌜	⌜	PROPN
ejpam-6331	198	31	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	32	⌝	⌝	PROPN
ejpam-6331	198	33	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	198	34	⌜	⌜	PROPN
ejpam-6331	198	35	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	36	⌝	⌝	PROPN
ejpam-6331	198	37	)	)	PUNCT
ejpam-6331	198	38	≥	≥	NOUN
ejpam-6331	198	39	min{∅̃c((	min{∅̃c((	PROPN
ejpam-6331	198	40	⌜	⌜	PROPN
ejpam-6331	198	41	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	42	⌝	⌝	PROPN
ejpam-6331	198	43	∗	∗	NOUN
ejpam-6331	198	44	⌜	⌜	PROPN
ejpam-6331	198	45	κ̃	κ̃	PROPN
ejpam-6331	198	46	⌝	⌝	PROPN
ejpam-6331	198	47	)∗	)∗	PROPN
ejpam-6331	198	48	⌜	⌜	PROPN
ejpam-6331	198	49	ϑ̃	ϑ̃	PROPN
ejpam-6331	198	50	⌝	⌝	PROPN
ejpam-6331	198	51	)eiω̃c((	)eiω̃c((	PROPN
ejpam-6331	198	52	⌜	⌜	PROPN
ejpam-6331	198	53	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	54	⌝	⌝	PROPN
ejpam-6331	198	55	∗	∗	NOUN
ejpam-6331	198	56	⌜	⌜	PROPN
ejpam-6331	198	57	κ̃	κ̃	PROPN
ejpam-6331	198	58	⌝	⌝	PROPN
ejpam-6331	198	59	)∗	)∗	PROPN
ejpam-6331	198	60	⌜	⌜	PROPN
ejpam-6331	198	61	ϑ̃	ϑ̃	PROPN
ejpam-6331	198	62	⌝	⌝	PROPN
ejpam-6331	198	63	)	)	PUNCT
ejpam-6331	198	64	,	,	PUNCT
ejpam-6331	198	65	∅̃c(	∅̃c(	NOUN
ejpam-6331	198	66	⌜	⌜	SYM
ejpam-6331	198	67	ϑ̃	ϑ̃	PROPN
ejpam-6331	198	68	⌝	⌝	PROPN
ejpam-6331	198	69	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	198	70	⌜	⌜	PROPN
ejpam-6331	198	71	ϑ̃	ϑ̃	PROPN
ejpam-6331	198	72	⌝	⌝	PROPN
ejpam-6331	198	73	)	)	PUNCT
ejpam-6331	198	74	}	}	PUNCT
ejpam-6331	198	75	,	,	PUNCT
ejpam-6331	198	76	(	(	PUNCT
ejpam-6331	198	77	cifbi-3	cifbi-3	NOUN
ejpam-6331	198	78	)	)	PUNCT
ejpam-6331	198	79	φ̃c(	φ̃c(	NOUN
ejpam-6331	198	80	⌜	⌜	NOUN
ejpam-6331	198	81	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	82	⌝	⌝	PROPN
ejpam-6331	198	83	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	198	84	⌜	⌜	PROPN
ejpam-6331	198	85	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	86	⌝	⌝	PROPN
ejpam-6331	198	87	)	)	PUNCT
ejpam-6331	198	88	≤	≤	PUNCT
ejpam-6331	198	89	max{φ̃c((	max{φ̃c((	PROPN
ejpam-6331	198	90	⌜	⌜	PROPN
ejpam-6331	198	91	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	92	⌝	⌝	PROPN
ejpam-6331	198	93	∗	∗	NOUN
ejpam-6331	198	94	⌜	⌜	PROPN
ejpam-6331	198	95	κ̃	κ̃	PROPN
ejpam-6331	198	96	⌝	⌝	PROPN
ejpam-6331	198	97	)∗	)∗	PROPN
ejpam-6331	198	98	⌜	⌜	PROPN
ejpam-6331	198	99	ϑ̃	ϑ̃	PROPN
ejpam-6331	198	100	⌝	⌝	PROPN
ejpam-6331	198	101	)eiθ̃c((	)eiθ̃c((	PROPN
ejpam-6331	198	102	⌜	⌜	PROPN
ejpam-6331	198	103	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	104	⌝	⌝	PROPN
ejpam-6331	198	105	∗	∗	NOUN
ejpam-6331	198	106	⌜	⌜	PROPN
ejpam-6331	198	107	κ̃	κ̃	PROPN
ejpam-6331	198	108	⌝	⌝	PROPN
ejpam-6331	198	109	)∗	)∗	PROPN
ejpam-6331	198	110	⌜	⌜	PROPN
ejpam-6331	198	111	ϑ̃	ϑ̃	PROPN
ejpam-6331	198	112	⌝	⌝	PROPN
ejpam-6331	198	113	)	)	PUNCT
ejpam-6331	198	114	,	,	PUNCT
ejpam-6331	198	115	φ̃c(	φ̃c(	PROPN
ejpam-6331	198	116	⌜	⌜	PROPN
ejpam-6331	198	117	ϑ̃	ϑ̃	PROPN
ejpam-6331	198	118	⌝	⌝	PROPN
ejpam-6331	198	119	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	198	120	⌜	⌜	PROPN
ejpam-6331	198	121	ϑ̃	ϑ̃	PROPN
ejpam-6331	198	122	⌝	⌝	PROPN
ejpam-6331	198	123	)	)	PUNCT
ejpam-6331	198	124	}	}	PUNCT
ejpam-6331	198	125	,	,	PUNCT
ejpam-6331	198	126	for	for	ADP
ejpam-6331	198	127	all	all	DET
ejpam-6331	198	128	⌜	⌜	PROPN
ejpam-6331	198	129	ϱ̃	ϱ̃	PROPN
ejpam-6331	198	130	⌝	⌝	PROPN
ejpam-6331	198	131	,	,	PUNCT
ejpam-6331	198	132	⌜	⌜	PROPN
ejpam-6331	198	133	ϑ̃	ϑ̃	PROPN
ejpam-6331	198	134	⌝	⌝	PROPN
ejpam-6331	198	135	,	,	PUNCT
ejpam-6331	198	136	⌜	⌜	PROPN
ejpam-6331	198	137	κ̃	κ̃	PROPN
ejpam-6331	198	138	⌝	⌝	PROPN
ejpam-6331	198	139	∈	∈	PROPN
ejpam-6331	198	140	x	x	X
ejpam-6331	198	141	.	.	PUNCT
ejpam-6331	199	1	theorem	theorem	NOUN
ejpam-6331	199	2	3	3	X
ejpam-6331	199	3	.	.	PUNCT
ejpam-6331	200	1	let	let	AUX
ejpam-6331	200	2	c	c	NOUN
ejpam-6331	200	3	=	=	SYM
ejpam-6331	200	4	(	(	PUNCT
ejpam-6331	200	5	∅̃ceiω̃c	∅̃ceiω̃c	NUM
ejpam-6331	200	6	,	,	PUNCT
ejpam-6331	200	7	φ̃ce	φ̃ce	PROPN
ejpam-6331	200	8	iθ̃c	iθ̃c	PROPN
ejpam-6331	200	9	)	)	PUNCT
ejpam-6331	200	10	be	be	VERB
ejpam-6331	200	11	a	a	DET
ejpam-6331	200	12	cif	cif	PROPN
ejpam-6331	200	13	-	-	PUNCT
ejpam-6331	200	14	set	set	NOUN
ejpam-6331	200	15	.	.	PUNCT
ejpam-6331	201	1	then	then	ADV
ejpam-6331	201	2	the	the	DET
ejpam-6331	201	3	following	follow	VERB
ejpam-6331	201	4	conditions	condition	NOUN
ejpam-6331	201	5	are	be	AUX
ejpam-6331	201	6	equivalent	equivalent	ADJ
ejpam-6331	201	7	:	:	PUNCT
ejpam-6331	201	8	(	(	PUNCT
ejpam-6331	201	9	1	1	X
ejpam-6331	201	10	)	)	PUNCT
ejpam-6331	201	11	c	c	NOUN
ejpam-6331	201	12	is	be	AUX
ejpam-6331	201	13	a	a	DET
ejpam-6331	201	14	cif	cif	PROPN
ejpam-6331	201	15	-	-	PUNCT
ejpam-6331	201	16	ideal	ideal	NOUN
ejpam-6331	201	17	of	of	ADP
ejpam-6331	201	18	x	x	X
ejpam-6331	201	19	.	.	PUNCT
ejpam-6331	202	1	(	(	PUNCT
ejpam-6331	202	2	2	2	X
ejpam-6331	202	3	)	)	PUNCT
ejpam-6331	202	4	c	c	NOUN
ejpam-6331	202	5	is	be	AUX
ejpam-6331	202	6	a	a	DET
ejpam-6331	202	7	cifqa	cifqa	NOUN
ejpam-6331	202	8	-	-	PUNCT
ejpam-6331	202	9	ideal	ideal	NOUN
ejpam-6331	202	10	of	of	ADP
ejpam-6331	202	11	x	x	X
ejpam-6331	202	12	.	.	PUNCT
ejpam-6331	203	1	(	(	PUNCT
ejpam-6331	203	2	3	3	X
ejpam-6331	203	3	)	)	PUNCT
ejpam-6331	203	4	c	c	NOUN
ejpam-6331	203	5	is	be	AUX
ejpam-6331	203	6	a	a	DET
ejpam-6331	203	7	cifb	cifb	NOUN
ejpam-6331	203	8	-	-	PUNCT
ejpam-6331	203	9	ideal	ideal	NOUN
ejpam-6331	203	10	of	of	ADP
ejpam-6331	203	11	x	x	X
ejpam-6331	203	12	.	.	PUNCT
ejpam-6331	204	1	proof	proof	NOUN
ejpam-6331	204	2	.	.	PUNCT
ejpam-6331	205	1	the	the	DET
ejpam-6331	205	2	diagram	diagram	NOUN
ejpam-6331	205	3	below	below	ADV
ejpam-6331	205	4	illustrates	illustrate	VERB
ejpam-6331	205	5	the	the	DET
ejpam-6331	205	6	equivalence	equivalence	NOUN
ejpam-6331	205	7	between	between	ADP
ejpam-6331	205	8	the	the	DET
ejpam-6331	205	9	three	three	NUM
ejpam-6331	205	10	types	type	NOUN
ejpam-6331	205	11	of	of	ADP
ejpam-6331	205	12	ideals	ideal	NOUN
ejpam-6331	205	13	.	.	PUNCT
ejpam-6331	206	1	cif	cif	PROPN
ejpam-6331	206	2	-	-	PUNCT
ejpam-6331	206	3	ideal	ideal	PROPN
ejpam-6331	206	4	cifqa	cifqa	NOUN
ejpam-6331	206	5	-	-	PUNCT
ejpam-6331	206	6	ideal	ideal	NOUN
ejpam-6331	206	7	cifb	cifb	NOUN
ejpam-6331	206	8	-	-	PUNCT
ejpam-6331	206	9	ideal	ideal	NOUN
ejpam-6331	206	10	we	we	PRON
ejpam-6331	206	11	prove	prove	VERB
ejpam-6331	206	12	the	the	DET
ejpam-6331	206	13	equivalences	equivalence	NOUN
ejpam-6331	206	14	by	by	ADP
ejpam-6331	206	15	showing	show	VERB
ejpam-6331	206	16	the	the	DET
ejpam-6331	206	17	implications	implication	NOUN
ejpam-6331	206	18	(	(	PUNCT
ejpam-6331	206	19	1	1	X
ejpam-6331	206	20	)	)	PUNCT
ejpam-6331	206	21	⇒	⇒	NOUN
ejpam-6331	206	22	(	(	PUNCT
ejpam-6331	206	23	2	2	NUM
ejpam-6331	206	24	)	)	PUNCT
ejpam-6331	206	25	⇒	⇒	NOUN
ejpam-6331	206	26	(	(	PUNCT
ejpam-6331	206	27	3	3	NUM
ejpam-6331	206	28	)	)	PUNCT
ejpam-6331	206	29	⇒	⇒	NOUN
ejpam-6331	206	30	(	(	PUNCT
ejpam-6331	206	31	1	1	NUM
ejpam-6331	206	32	)	)	PUNCT
ejpam-6331	206	33	.	.	PUNCT
ejpam-6331	207	1	(	(	PUNCT
ejpam-6331	207	2	1	1	X
ejpam-6331	207	3	)	)	PUNCT
ejpam-6331	207	4	⇒	⇒	NOUN
ejpam-6331	207	5	(	(	PUNCT
ejpam-6331	207	6	2	2	X
ejpam-6331	207	7	)	)	PUNCT
ejpam-6331	207	8	assume	assume	VERB
ejpam-6331	207	9	that	that	SCONJ
ejpam-6331	207	10	c	c	PROPN
ejpam-6331	207	11	is	be	AUX
ejpam-6331	207	12	a	a	DET
ejpam-6331	207	13	cif	cif	PROPN
ejpam-6331	207	14	-	-	PUNCT
ejpam-6331	207	15	ideal	ideal	NOUN
ejpam-6331	207	16	.	.	PUNCT
ejpam-6331	208	1	we	we	PRON
ejpam-6331	208	2	show	show	VERB
ejpam-6331	208	3	it	it	PRON
ejpam-6331	208	4	is	be	AUX
ejpam-6331	208	5	a	a	DET
ejpam-6331	208	6	cifqa	cifqa	NOUN
ejpam-6331	208	7	-	-	PUNCT
ejpam-6331	208	8	ideal	ideal	NOUN
ejpam-6331	208	9	.	.	PUNCT
ejpam-6331	209	1	for	for	ADP
ejpam-6331	209	2	any	any	DET
ejpam-6331	209	3	⌜	⌜	PROPN
ejpam-6331	209	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	209	5	⌝	⌝	PROPN
ejpam-6331	209	6	,	,	PUNCT
ejpam-6331	209	7	⌜	⌜	PROPN
ejpam-6331	209	8	ϑ̃	ϑ̃	PROPN
ejpam-6331	209	9	⌝	⌝	PROPN
ejpam-6331	209	10	,	,	PUNCT
ejpam-6331	209	11	⌜	⌜	PROPN
ejpam-6331	209	12	κ̃	κ̃	PROPN
ejpam-6331	209	13	⌝	⌝	PROPN
ejpam-6331	209	14	∈	∈	PROPN
ejpam-6331	209	15	x	x	X
ejpam-6331	209	16	,	,	PUNCT
ejpam-6331	209	17	by	by	ADP
ejpam-6331	209	18	definition	definition	NOUN
ejpam-6331	209	19	6	6	NUM
ejpam-6331	209	20	,	,	PUNCT
ejpam-6331	209	21	we	we	PRON
ejpam-6331	209	22	have	have	VERB
ejpam-6331	209	23	∅̃c(	∅̃c(	NOUN
ejpam-6331	209	24	⌜	⌜	NOUN
ejpam-6331	209	25	ϱ̃	ϱ̃	PROPN
ejpam-6331	209	26	⌝	⌝	PROPN
ejpam-6331	209	27	∗	∗	NOUN
ejpam-6331	209	28	⌜	⌜	PROPN
ejpam-6331	209	29	κ̃	κ̃	PROPN
ejpam-6331	209	30	⌝	⌝	PROPN
ejpam-6331	209	31	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	209	32	⌜	⌜	PROPN
ejpam-6331	209	33	ϱ̃	ϱ̃	PROPN
ejpam-6331	209	34	⌝	⌝	PROPN
ejpam-6331	209	35	∗	∗	NOUN
ejpam-6331	209	36	⌜	⌜	PROPN
ejpam-6331	209	37	κ̃	κ̃	PROPN
ejpam-6331	209	38	⌝	⌝	PROPN
ejpam-6331	209	39	)	)	PUNCT
ejpam-6331	209	40	≥	≥	NOUN
ejpam-6331	209	41	min{∅̃c((	min{∅̃c((	PROPN
ejpam-6331	209	42	⌜	⌜	PROPN
ejpam-6331	209	43	ϱ̃	ϱ̃	PROPN
ejpam-6331	209	44	⌝	⌝	PROPN
ejpam-6331	209	45	∗	∗	NOUN
ejpam-6331	209	46	⌜	⌜	PROPN
ejpam-6331	209	47	κ̃	κ̃	PROPN
ejpam-6331	209	48	⌝	⌝	PROPN
ejpam-6331	209	49	)	)	PUNCT
ejpam-6331	209	50	∗	∗	NOUN
ejpam-6331	209	51	⌜	⌜	PROPN
ejpam-6331	209	52	ϑ̃	ϑ̃	PROPN
ejpam-6331	209	53	⌝	⌝	PROPN
ejpam-6331	209	54	)eiω̃c((	)eiω̃c((	PROPN
ejpam-6331	209	55	⌜	⌜	PROPN
ejpam-6331	209	56	ϱ̃	ϱ̃	PROPN
ejpam-6331	209	57	⌝	⌝	PROPN
ejpam-6331	209	58	∗	∗	NOUN
ejpam-6331	209	59	⌜	⌜	PROPN
ejpam-6331	209	60	κ̃	κ̃	PROPN
ejpam-6331	209	61	⌝	⌝	PROPN
ejpam-6331	209	62	)∗	)∗	PROPN
ejpam-6331	209	63	⌜	⌜	PROPN
ejpam-6331	209	64	ϑ̃	ϑ̃	PROPN
ejpam-6331	209	65	⌝	⌝	PROPN
ejpam-6331	209	66	)	)	PUNCT
ejpam-6331	209	67	,	,	PUNCT
ejpam-6331	209	68	∅̃c(	∅̃c(	NOUN
ejpam-6331	209	69	⌜	⌜	SYM
ejpam-6331	209	70	ϑ̃	ϑ̃	PROPN
ejpam-6331	209	71	⌝	⌝	PROPN
ejpam-6331	209	72	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	209	73	⌜	⌜	PROPN
ejpam-6331	209	74	ϑ̃	ϑ̃	PROPN
ejpam-6331	209	75	⌝	⌝	PROPN
ejpam-6331	209	76	)	)	PUNCT
ejpam-6331	209	77	}	}	PUNCT
ejpam-6331	209	78	.	.	PUNCT
ejpam-6331	210	1	setting	set	VERB
ejpam-6331	210	2	⌜	⌜	PROPN
ejpam-6331	210	3	ϑ̃	ϑ̃	PROPN
ejpam-6331	210	4	⌝	⌝	PROPN
ejpam-6331	210	5	=	=	SYM
ejpam-6331	210	6	0	0	NUM
ejpam-6331	210	7	,	,	PUNCT
ejpam-6331	210	8	we	we	PRON
ejpam-6331	210	9	get	get	VERB
ejpam-6331	210	10	∅̃c(	∅̃c(	NOUN
ejpam-6331	210	11	⌜	⌜	NOUN
ejpam-6331	210	12	ϱ̃	ϱ̃	PROPN
ejpam-6331	210	13	⌝	⌝	PROPN
ejpam-6331	210	14	∗	∗	NOUN
ejpam-6331	210	15	⌜	⌜	PROPN
ejpam-6331	210	16	κ̃	κ̃	PROPN
ejpam-6331	210	17	⌝	⌝	PROPN
ejpam-6331	210	18	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	210	19	⌜	⌜	PROPN
ejpam-6331	210	20	ϱ̃	ϱ̃	PROPN
ejpam-6331	210	21	⌝	⌝	PROPN
ejpam-6331	210	22	∗	∗	NOUN
ejpam-6331	210	23	⌜	⌜	PROPN
ejpam-6331	210	24	κ̃	κ̃	PROPN
ejpam-6331	210	25	⌝	⌝	PROPN
ejpam-6331	210	26	)	)	PUNCT
ejpam-6331	210	27	≥	≥	NOUN
ejpam-6331	210	28	min{∅̃c((	min{∅̃c((	PROPN
ejpam-6331	210	29	⌜	⌜	PROPN
ejpam-6331	210	30	ϱ̃	ϱ̃	PROPN
ejpam-6331	210	31	⌝	⌝	PROPN
ejpam-6331	211	1	∗	∗	NOUN
ejpam-6331	211	2	⌜	⌜	PROPN
ejpam-6331	211	3	κ̃	κ̃	PROPN
ejpam-6331	211	4	⌝	⌝	PROPN
ejpam-6331	211	5	)	)	PUNCT
ejpam-6331	211	6	∗	∗	NOUN
ejpam-6331	211	7	0)eiω̃c((	0)eiω̃c((	NOUN
ejpam-6331	211	8	⌜	⌜	PUNCT
ejpam-6331	211	9	ϱ̃	ϱ̃	PROPN
ejpam-6331	211	10	⌝	⌝	PROPN
ejpam-6331	211	11	∗	∗	NOUN
ejpam-6331	211	12	⌜	⌜	PROPN
ejpam-6331	211	13	κ̃	κ̃	PROPN
ejpam-6331	211	14	⌝	⌝	PROPN
ejpam-6331	211	15	)∗0	)∗0	PROPN
ejpam-6331	211	16	,	,	PUNCT
ejpam-6331	211	17	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	NOUN
ejpam-6331	211	18	)	)	PUNCT
ejpam-6331	211	19	}	}	PUNCT
ejpam-6331	211	20	.	.	PUNCT
ejpam-6331	212	1	since	since	SCONJ
ejpam-6331	212	2	(	(	PUNCT
ejpam-6331	212	3	⌜	⌜	NUM
ejpam-6331	212	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	212	5	⌝	⌝	PROPN
ejpam-6331	212	6	∗	∗	NOUN
ejpam-6331	212	7	⌜	⌜	PROPN
ejpam-6331	212	8	κ̃	κ̃	PROPN
ejpam-6331	212	9	⌝	⌝	PROPN
ejpam-6331	212	10	)	)	PUNCT
ejpam-6331	212	11	∗	∗	NOUN
ejpam-6331	212	12	0	0	NUM
ejpam-6331	213	1	=	=	SYM
ejpam-6331	213	2	⌜	⌜	NUM
ejpam-6331	213	3	ϱ̃	ϱ̃	PROPN
ejpam-6331	213	4	⌝	⌝	PROPN
ejpam-6331	213	5	∗	∗	NOUN
ejpam-6331	213	6	⌜	⌜	PROPN
ejpam-6331	213	7	κ̃	κ̃	PROPN
ejpam-6331	213	8	⌝	⌝	PROPN
ejpam-6331	213	9	and	and	CCONJ
ejpam-6331	213	10	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	NOUN
ejpam-6331	213	11	)	)	PUNCT
ejpam-6331	213	12	≥	≥	NOUN
ejpam-6331	213	13	∅̃c(	∅̃c(	NOUN
ejpam-6331	213	14	⌜	⌜	SYM
ejpam-6331	213	15	ϑ̃	ϑ̃	PROPN
ejpam-6331	213	16	⌝	⌝	PROPN
ejpam-6331	213	17	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	213	18	⌜	⌜	PROPN
ejpam-6331	213	19	ϑ̃	ϑ̃	PROPN
ejpam-6331	213	20	⌝	⌝	PROPN
ejpam-6331	213	21	)	)	PUNCT
ejpam-6331	213	22	for	for	ADP
ejpam-6331	213	23	any	any	DET
ejpam-6331	213	24	⌜	⌜	PROPN
ejpam-6331	213	25	ϑ̃	ϑ̃	PROPN
ejpam-6331	213	26	⌝	⌝	PROPN
ejpam-6331	213	27	∈	∈	PROPN
ejpam-6331	213	28	x	x	X
ejpam-6331	213	29	,	,	PUNCT
ejpam-6331	213	30	this	this	DET
ejpam-6331	213	31	simplifies	simplifie	NOUN
ejpam-6331	213	32	to	to	PART
ejpam-6331	213	33	∅̃c(	∅̃c(	VERB
ejpam-6331	213	34	⌜	⌜	PROPN
ejpam-6331	213	35	ϱ̃	ϱ̃	PROPN
ejpam-6331	213	36	⌝	⌝	PROPN
ejpam-6331	213	37	∗	∗	NOUN
ejpam-6331	213	38	⌜	⌜	PROPN
ejpam-6331	213	39	κ̃	κ̃	PROPN
ejpam-6331	213	40	⌝	⌝	PROPN
ejpam-6331	213	41	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	213	42	⌜	⌜	PROPN
ejpam-6331	213	43	ϱ̃	ϱ̃	PROPN
ejpam-6331	213	44	⌝	⌝	PROPN
ejpam-6331	213	45	∗	∗	NOUN
ejpam-6331	213	46	⌜	⌜	PROPN
ejpam-6331	213	47	κ̃	κ̃	PROPN
ejpam-6331	213	48	⌝	⌝	PROPN
ejpam-6331	213	49	)	)	PUNCT
ejpam-6331	213	50	≥	≥	NOUN
ejpam-6331	214	1	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	214	2	⌜	⌜	PROPN
ejpam-6331	215	1	ϱ̃	ϱ̃	PROPN
ejpam-6331	215	2	⌝	⌝	PROPN
ejpam-6331	215	3	∗	∗	NOUN
ejpam-6331	215	4	⌜	⌜	PROPN
ejpam-6331	215	5	κ̃	κ̃	PROPN
ejpam-6331	215	6	⌝	⌝	PROPN
ejpam-6331	215	7	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	215	8	⌜	⌜	PROPN
ejpam-6331	215	9	ϱ̃	ϱ̃	PROPN
ejpam-6331	215	10	⌝	⌝	PROPN
ejpam-6331	215	11	∗	∗	NOUN
ejpam-6331	215	12	⌜	⌜	PROPN
ejpam-6331	215	13	κ̃	κ̃	PROPN
ejpam-6331	215	14	⌝	⌝	PROPN
ejpam-6331	215	15	)	)	PUNCT
ejpam-6331	215	16	,	,	PUNCT
ejpam-6331	215	17	∅̃c(0)eiω̃c(0	∅̃c(0)eiω̃c(0	NOUN
ejpam-6331	215	18	)	)	PUNCT
ejpam-6331	215	19	}	}	PUNCT
ejpam-6331	215	20	t.	t.	PROPN
ejpam-6331	215	21	ramesh	ramesh	PROPN
ejpam-6331	215	22	,	,	PUNCT
ejpam-6331	215	23	m.	m.	NOUN
ejpam-6331	215	24	balamurugan	balamurugan	PROPN
ejpam-6331	215	25	,	,	PUNCT
ejpam-6331	215	26	a.	a.	NOUN
ejpam-6331	215	27	iampan	iampan	PROPN
ejpam-6331	215	28	/	/	SYM
ejpam-6331	215	29	eur	eur	PROPN
ejpam-6331	215	30	.	.	PUNCT
ejpam-6331	216	1	j.	j.	PROPN
ejpam-6331	216	2	pure	pure	PROPN
ejpam-6331	216	3	appl	appl	PROPN
ejpam-6331	216	4	.	.	PROPN
ejpam-6331	216	5	math	math	PROPN
ejpam-6331	216	6	,	,	PUNCT
ejpam-6331	216	7	18	18	NUM
ejpam-6331	216	8	(	(	PUNCT
ejpam-6331	216	9	3	3	NUM
ejpam-6331	216	10	)	)	PUNCT
ejpam-6331	216	11	(	(	PUNCT
ejpam-6331	216	12	2025	2025	NUM
ejpam-6331	216	13	)	)	PUNCT
ejpam-6331	216	14	,	,	PUNCT
ejpam-6331	216	15	6331	6331	NUM
ejpam-6331	216	16	12	12	NUM
ejpam-6331	216	17	of	of	ADP
ejpam-6331	216	18	14	14	NUM
ejpam-6331	216	19	=	=	SYM
ejpam-6331	216	20	∅̃c(	∅̃c(	NOUN
ejpam-6331	216	21	⌜	⌜	NOUN
ejpam-6331	216	22	ϱ̃	ϱ̃	PROPN
ejpam-6331	216	23	⌝	⌝	PROPN
ejpam-6331	216	24	∗	∗	NOUN
ejpam-6331	216	25	⌜	⌜	PROPN
ejpam-6331	216	26	κ̃	κ̃	PROPN
ejpam-6331	216	27	⌝	⌝	PROPN
ejpam-6331	216	28	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	216	29	⌜	⌜	PROPN
ejpam-6331	216	30	ϱ̃	ϱ̃	PROPN
ejpam-6331	216	31	⌝	⌝	PROPN
ejpam-6331	216	32	∗	∗	NOUN
ejpam-6331	216	33	⌜	⌜	PROPN
ejpam-6331	216	34	κ̃	κ̃	PROPN
ejpam-6331	216	35	⌝	⌝	PROPN
ejpam-6331	216	36	)	)	PUNCT
ejpam-6331	216	37	.	.	PUNCT
ejpam-6331	217	1	thus	thus	ADV
ejpam-6331	217	2	,	,	PUNCT
ejpam-6331	217	3	cifqai-1	cifqai-1	PROPN
ejpam-6331	217	4	is	be	AUX
ejpam-6331	217	5	satisfied	satisfied	ADJ
ejpam-6331	217	6	.	.	PUNCT
ejpam-6331	218	1	similarly	similarly	ADV
ejpam-6331	218	2	,	,	PUNCT
ejpam-6331	218	3	for	for	ADP
ejpam-6331	218	4	the	the	DET
ejpam-6331	218	5	non	non	ADJ
ejpam-6331	218	6	-	-	ADJ
ejpam-6331	218	7	membership	membership	ADJ
ejpam-6331	218	8	function	function	NOUN
ejpam-6331	218	9	,	,	PUNCT
ejpam-6331	218	10	φ̃c(	φ̃c(	VERB
ejpam-6331	218	11	⌜	⌜	NOUN
ejpam-6331	218	12	ϱ̃	ϱ̃	PROPN
ejpam-6331	218	13	⌝	⌝	PROPN
ejpam-6331	218	14	∗	∗	NOUN
ejpam-6331	218	15	⌜	⌜	PROPN
ejpam-6331	218	16	κ̃	κ̃	PROPN
ejpam-6331	218	17	⌝	⌝	PROPN
ejpam-6331	218	18	)eiθ̃c(	)eiθ̃c(	ADJ
ejpam-6331	218	19	⌜	⌜	PROPN
ejpam-6331	218	20	ϱ̃	ϱ̃	PROPN
ejpam-6331	218	21	⌝	⌝	PROPN
ejpam-6331	218	22	∗	∗	NOUN
ejpam-6331	218	23	⌜	⌜	PROPN
ejpam-6331	218	24	κ̃	κ̃	PROPN
ejpam-6331	218	25	⌝	⌝	PROPN
ejpam-6331	218	26	)	)	PUNCT
ejpam-6331	218	27	≤	≤	PUNCT
ejpam-6331	218	28	max{φ̃c((	max{φ̃c((	PROPN
ejpam-6331	218	29	⌜	⌜	PROPN
ejpam-6331	218	30	ϱ̃	ϱ̃	PROPN
ejpam-6331	218	31	⌝	⌝	PROPN
ejpam-6331	218	32	∗	∗	NOUN
ejpam-6331	218	33	⌜	⌜	PROPN
ejpam-6331	218	34	κ̃	κ̃	PROPN
ejpam-6331	218	35	⌝	⌝	PROPN
ejpam-6331	218	36	)∗	)∗	PROPN
ejpam-6331	218	37	⌜	⌜	PROPN
ejpam-6331	218	38	ϑ̃	ϑ̃	PROPN
ejpam-6331	218	39	⌝	⌝	PROPN
ejpam-6331	218	40	)eiθ̃c((	)eiθ̃c((	PROPN
ejpam-6331	218	41	⌜	⌜	PROPN
ejpam-6331	218	42	ϱ̃	ϱ̃	PROPN
ejpam-6331	218	43	⌝	⌝	PROPN
ejpam-6331	218	44	∗	∗	NOUN
ejpam-6331	218	45	⌜	⌜	PROPN
ejpam-6331	218	46	κ̃	κ̃	PROPN
ejpam-6331	218	47	⌝	⌝	PROPN
ejpam-6331	218	48	)∗	)∗	PROPN
ejpam-6331	218	49	⌜	⌜	PROPN
ejpam-6331	218	50	ϑ̃	ϑ̃	PROPN
ejpam-6331	218	51	⌝	⌝	PROPN
ejpam-6331	218	52	)	)	PUNCT
ejpam-6331	218	53	,	,	PUNCT
ejpam-6331	218	54	φ̃c(	φ̃c(	AUX
ejpam-6331	218	55	⌜	⌜	PROPN
ejpam-6331	218	56	ϑ̃	ϑ̃	PROPN
ejpam-6331	218	57	⌝	⌝	PROPN
ejpam-6331	218	58	)e	)e	NOUN
ejpam-6331	218	59	iθ̃c(	iθ̃c(	NOUN
ejpam-6331	218	60	⌜	⌜	PROPN
ejpam-6331	218	61	ϑ̃	ϑ̃	PROPN
ejpam-6331	218	62	⌝	⌝	PROPN
ejpam-6331	218	63	)	)	PUNCT
ejpam-6331	218	64	}	}	PUNCT
ejpam-6331	218	65	.	.	PUNCT
ejpam-6331	219	1	setting	set	VERB
ejpam-6331	219	2	⌜	⌜	PROPN
ejpam-6331	219	3	ϑ̃	ϑ̃	PROPN
ejpam-6331	219	4	⌝	⌝	PROPN
ejpam-6331	219	5	=	=	SYM
ejpam-6331	219	6	0	0	PUNCT
ejpam-6331	219	7	and	and	CCONJ
ejpam-6331	219	8	using	use	VERB
ejpam-6331	219	9	φ̃c(0)e	φ̃c(0)e	NUM
ejpam-6331	219	10	iθ̃c(0	iθ̃c(0	NOUN
ejpam-6331	219	11	)	)	PUNCT
ejpam-6331	219	12	≤	≤	NOUN
ejpam-6331	219	13	φ̃c(	φ̃c(	NOUN
ejpam-6331	219	14	⌜	⌜	PROPN
ejpam-6331	219	15	ϑ̃	ϑ̃	PROPN
ejpam-6331	219	16	⌝	⌝	PROPN
ejpam-6331	219	17	)eiθ̃c(	)eiθ̃c(	PROPN
ejpam-6331	219	18	⌜	⌜	PROPN
ejpam-6331	219	19	ϑ̃	ϑ̃	PROPN
ejpam-6331	219	20	⌝	⌝	PROPN
ejpam-6331	219	21	)	)	PUNCT
ejpam-6331	219	22	,	,	PUNCT
ejpam-6331	219	23	we	we	PRON
ejpam-6331	219	24	obtain	obtain	VERB
ejpam-6331	219	25	the	the	DET
ejpam-6331	219	26	required	required	ADJ
ejpam-6331	219	27	condition	condition	NOUN
ejpam-6331	219	28	.	.	PUNCT
ejpam-6331	220	1	(	(	PUNCT
ejpam-6331	220	2	2	2	X
ejpam-6331	220	3	)	)	PUNCT
ejpam-6331	220	4	⇒	⇒	NOUN
ejpam-6331	220	5	(	(	PUNCT
ejpam-6331	220	6	3	3	X
ejpam-6331	220	7	)	)	PUNCT
ejpam-6331	220	8	assume	assume	VERB
ejpam-6331	220	9	that	that	SCONJ
ejpam-6331	220	10	c	c	PROPN
ejpam-6331	220	11	is	be	AUX
ejpam-6331	220	12	a	a	DET
ejpam-6331	220	13	cifqa	cifqa	NOUN
ejpam-6331	220	14	-	-	PUNCT
ejpam-6331	220	15	ideal	ideal	NOUN
ejpam-6331	220	16	.	.	PUNCT
ejpam-6331	221	1	we	we	PRON
ejpam-6331	221	2	show	show	VERB
ejpam-6331	221	3	it	it	PRON
ejpam-6331	221	4	is	be	AUX
ejpam-6331	221	5	a	a	DET
ejpam-6331	221	6	cifb	cifb	NOUN
ejpam-6331	221	7	-	-	PUNCT
ejpam-6331	221	8	ideal	ideal	NOUN
ejpam-6331	221	9	.	.	PUNCT
ejpam-6331	222	1	for	for	ADP
ejpam-6331	222	2	any	any	DET
ejpam-6331	222	3	⌜	⌜	PROPN
ejpam-6331	222	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	222	5	⌝	⌝	PROPN
ejpam-6331	222	6	,	,	PUNCT
ejpam-6331	222	7	⌜	⌜	PROPN
ejpam-6331	222	8	ϑ̃	ϑ̃	PROPN
ejpam-6331	222	9	⌝	⌝	PROPN
ejpam-6331	222	10	,	,	PUNCT
ejpam-6331	222	11	⌜	⌜	PROPN
ejpam-6331	222	12	κ̃	κ̃	PROPN
ejpam-6331	222	13	⌝	⌝	PROPN
ejpam-6331	222	14	∈	∈	PROPN
ejpam-6331	222	15	x	x	X
ejpam-6331	222	16	,	,	PUNCT
ejpam-6331	222	17	by	by	ADP
ejpam-6331	222	18	using	use	VERB
ejpam-6331	222	19	definition	definition	NOUN
ejpam-6331	222	20	7	7	NUM
ejpam-6331	222	21	,	,	PUNCT
ejpam-6331	222	22	we	we	PRON
ejpam-6331	222	23	have	have	VERB
ejpam-6331	222	24	∅̃c(	∅̃c(	NOUN
ejpam-6331	222	25	⌜	⌜	NOUN
ejpam-6331	222	26	ϱ̃	ϱ̃	PROPN
ejpam-6331	222	27	⌝	⌝	PROPN
ejpam-6331	222	28	∗	∗	NOUN
ejpam-6331	222	29	⌜	⌜	PROPN
ejpam-6331	222	30	κ̃	κ̃	PROPN
ejpam-6331	222	31	⌝	⌝	PROPN
ejpam-6331	222	32	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	222	33	⌜	⌜	PROPN
ejpam-6331	222	34	ϱ̃	ϱ̃	PROPN
ejpam-6331	222	35	⌝	⌝	PROPN
ejpam-6331	222	36	∗	∗	NOUN
ejpam-6331	222	37	⌜	⌜	PROPN
ejpam-6331	222	38	κ̃	κ̃	PROPN
ejpam-6331	222	39	⌝	⌝	PROPN
ejpam-6331	222	40	)	)	PUNCT
ejpam-6331	222	41	≥	≥	NOUN
ejpam-6331	223	1	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	223	2	⌜	⌜	PROPN
ejpam-6331	223	3	ϱ̃	ϱ̃	PROPN
ejpam-6331	223	4	⌝	⌝	PROPN
ejpam-6331	223	5	∗	∗	NOUN
ejpam-6331	223	6	(	(	PUNCT
ejpam-6331	223	7	⌜	⌜	PROPN
ejpam-6331	223	8	ϑ̃	ϑ̃	PROPN
ejpam-6331	223	9	⌝	⌝	PROPN
ejpam-6331	223	10	∗	∗	NOUN
ejpam-6331	223	11	⌜	⌜	PROPN
ejpam-6331	223	12	κ̃	κ̃	PROPN
ejpam-6331	223	13	⌝	⌝	PROPN
ejpam-6331	223	14	))eiω̃c(	))eiω̃c(	PROPN
ejpam-6331	223	15	⌜	⌜	PROPN
ejpam-6331	223	16	ϱ̃	ϱ̃	PROPN
ejpam-6331	223	17	⌝	⌝	PROPN
ejpam-6331	223	18	∗(	∗(	NOUN
ejpam-6331	223	19	⌜	⌜	PROPN
ejpam-6331	223	20	ϑ̃	ϑ̃	PROPN
ejpam-6331	223	21	⌝	⌝	PROPN
ejpam-6331	223	22	∗	∗	NOUN
ejpam-6331	223	23	⌜	⌜	PROPN
ejpam-6331	223	24	κ̃	κ̃	PROPN
ejpam-6331	223	25	⌝	⌝	PROPN
ejpam-6331	223	26	)	)	PUNCT
ejpam-6331	223	27	)	)	PUNCT
ejpam-6331	223	28	,	,	PUNCT
ejpam-6331	223	29	∅̃c(	∅̃c(	NOUN
ejpam-6331	223	30	⌜	⌜	SYM
ejpam-6331	223	31	ϑ̃	ϑ̃	PROPN
ejpam-6331	223	32	⌝	⌝	PROPN
ejpam-6331	223	33	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	223	34	⌜	⌜	PROPN
ejpam-6331	223	35	ϑ̃	ϑ̃	PROPN
ejpam-6331	223	36	⌝	⌝	PROPN
ejpam-6331	223	37	)	)	PUNCT
ejpam-6331	223	38	}	}	PUNCT
ejpam-6331	224	1	.	.	PUNCT
ejpam-6331	225	1	setting	set	VERB
ejpam-6331	225	2	⌜	⌜	PROPN
ejpam-6331	225	3	κ̃	κ̃	PROPN
ejpam-6331	225	4	⌝	⌝	PROPN
ejpam-6331	225	5	=	=	SYM
ejpam-6331	225	6	0	0	NUM
ejpam-6331	225	7	,	,	PUNCT
ejpam-6331	225	8	we	we	PRON
ejpam-6331	225	9	get	get	VERB
ejpam-6331	225	10	∅̃c(	∅̃c(	NOUN
ejpam-6331	225	11	⌜	⌜	NOUN
ejpam-6331	225	12	ϱ̃	ϱ̃	PROPN
ejpam-6331	225	13	⌝	⌝	PROPN
ejpam-6331	225	14	∗	∗	NOUN
ejpam-6331	225	15	0)eiω̃c(	0)eiω̃c(	NUM
ejpam-6331	225	16	⌜	⌜	NOUN
ejpam-6331	225	17	ϱ̃	ϱ̃	PROPN
ejpam-6331	225	18	⌝	⌝	PROPN
ejpam-6331	225	19	∗0	∗0	PROPN
ejpam-6331	225	20	)	)	PUNCT
ejpam-6331	225	21	≥	≥	NOUN
ejpam-6331	225	22	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	225	23	⌜	⌜	PROPN
ejpam-6331	225	24	ϱ̃	ϱ̃	PROPN
ejpam-6331	225	25	⌝	⌝	PROPN
ejpam-6331	225	26	∗	∗	NOUN
ejpam-6331	225	27	(	(	PUNCT
ejpam-6331	225	28	⌜	⌜	PROPN
ejpam-6331	225	29	ϑ̃	ϑ̃	PROPN
ejpam-6331	225	30	⌝	⌝	PROPN
ejpam-6331	225	31	∗	∗	NOUN
ejpam-6331	225	32	0))eiω̃c(	0))eiω̃c(	NOUN
ejpam-6331	225	33	⌜	⌜	NOUN
ejpam-6331	225	34	ϱ̃	ϱ̃	PROPN
ejpam-6331	225	35	⌝	⌝	PROPN
ejpam-6331	225	36	∗(	∗(	NOUN
ejpam-6331	225	37	⌜	⌜	PROPN
ejpam-6331	225	38	ϑ̃	ϑ̃	PROPN
ejpam-6331	225	39	⌝	⌝	PROPN
ejpam-6331	225	40	∗0	∗0	PROPN
ejpam-6331	225	41	)	)	PUNCT
ejpam-6331	225	42	)	)	PUNCT
ejpam-6331	225	43	,	,	PUNCT
ejpam-6331	225	44	∅̃c(	∅̃c(	NOUN
ejpam-6331	225	45	⌜	⌜	SYM
ejpam-6331	225	46	ϑ̃	ϑ̃	PROPN
ejpam-6331	225	47	⌝	⌝	PROPN
ejpam-6331	225	48	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	225	49	⌜	⌜	PROPN
ejpam-6331	225	50	ϑ̃	ϑ̃	PROPN
ejpam-6331	225	51	⌝	⌝	PROPN
ejpam-6331	225	52	)	)	PUNCT
ejpam-6331	225	53	}	}	PUNCT
ejpam-6331	225	54	.	.	PUNCT
ejpam-6331	226	1	since	since	SCONJ
ejpam-6331	226	2	⌜	⌜	PROPN
ejpam-6331	226	3	ϱ̃	ϱ̃	PROPN
ejpam-6331	226	4	⌝	⌝	PROPN
ejpam-6331	226	5	∗	∗	NOUN
ejpam-6331	226	6	0	0	NUM
ejpam-6331	227	1	=	=	SYM
ejpam-6331	227	2	⌜	⌜	PUNCT
ejpam-6331	227	3	ϱ̃	ϱ̃	PROPN
ejpam-6331	227	4	⌝	⌝	PROPN
ejpam-6331	227	5	and	and	CCONJ
ejpam-6331	227	6	⌜	⌜	PROPN
ejpam-6331	227	7	ϑ̃	ϑ̃	PROPN
ejpam-6331	227	8	⌝	⌝	PROPN
ejpam-6331	227	9	∗	∗	NOUN
ejpam-6331	227	10	0	0	NUM
ejpam-6331	228	1	=	=	SYM
ejpam-6331	228	2	⌜	⌜	PROPN
ejpam-6331	228	3	ϑ̃	ϑ̃	PROPN
ejpam-6331	228	4	⌝	⌝	PROPN
ejpam-6331	228	5	,	,	PUNCT
ejpam-6331	228	6	this	this	DET
ejpam-6331	228	7	simplifies	simplifie	NOUN
ejpam-6331	228	8	to	to	PART
ejpam-6331	228	9	∅̃c(	∅̃c(	VERB
ejpam-6331	228	10	⌜	⌜	PROPN
ejpam-6331	228	11	ϱ̃	ϱ̃	PROPN
ejpam-6331	228	12	⌝	⌝	PROPN
ejpam-6331	228	13	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	228	14	⌜	⌜	PROPN
ejpam-6331	228	15	ϱ̃	ϱ̃	PROPN
ejpam-6331	228	16	⌝	⌝	PROPN
ejpam-6331	228	17	)	)	PUNCT
ejpam-6331	228	18	≥	≥	NOUN
ejpam-6331	228	19	min{∅̃c(	min{∅̃c(	PROPN
ejpam-6331	228	20	⌜	⌜	PROPN
ejpam-6331	228	21	ϱ̃	ϱ̃	PROPN
ejpam-6331	228	22	⌝	⌝	PROPN
ejpam-6331	228	23	∗	∗	NOUN
ejpam-6331	228	24	⌜	⌜	PROPN
ejpam-6331	228	25	ϑ̃	ϑ̃	PROPN
ejpam-6331	228	26	⌝	⌝	PROPN
ejpam-6331	228	27	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	228	28	⌜	⌜	PROPN
ejpam-6331	228	29	ϱ̃	ϱ̃	PROPN
ejpam-6331	228	30	⌝	⌝	PROPN
ejpam-6331	228	31	∗	∗	NOUN
ejpam-6331	228	32	⌜	⌜	PROPN
ejpam-6331	228	33	ϑ̃	ϑ̃	PROPN
ejpam-6331	228	34	⌝	⌝	PROPN
ejpam-6331	228	35	)	)	PUNCT
ejpam-6331	228	36	,	,	PUNCT
ejpam-6331	228	37	∅̃c(	∅̃c(	NOUN
ejpam-6331	228	38	⌜	⌜	SYM
ejpam-6331	228	39	ϑ̃	ϑ̃	PROPN
ejpam-6331	228	40	⌝	⌝	PROPN
ejpam-6331	228	41	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	228	42	⌜	⌜	PROPN
ejpam-6331	228	43	ϑ̃	ϑ̃	PROPN
ejpam-6331	228	44	⌝	⌝	PROPN
ejpam-6331	228	45	)	)	PUNCT
ejpam-6331	228	46	}	}	PUNCT
ejpam-6331	228	47	.	.	PUNCT
ejpam-6331	229	1	this	this	PRON
ejpam-6331	229	2	is	be	AUX
ejpam-6331	229	3	the	the	DET
ejpam-6331	229	4	condition	condition	NOUN
ejpam-6331	229	5	for	for	ADP
ejpam-6331	229	6	cifb	cifb	NOUN
ejpam-6331	229	7	-	-	PUNCT
ejpam-6331	229	8	ideal	ideal	NOUN
ejpam-6331	229	9	when	when	SCONJ
ejpam-6331	229	10	⌜	⌜	PROPN
ejpam-6331	229	11	κ̃	κ̃	PROPN
ejpam-6331	229	12	⌝	⌝	PROPN
ejpam-6331	229	13	=	=	SYM
ejpam-6331	229	14	0	0	NUM
ejpam-6331	229	15	.	.	PUNCT
ejpam-6331	230	1	for	for	ADP
ejpam-6331	230	2	general	general	ADJ
ejpam-6331	230	3	⌜	⌜	PROPN
ejpam-6331	230	4	κ̃	κ̃	PROPN
ejpam-6331	230	5	⌝	⌝	PROPN
ejpam-6331	230	6	,	,	PUNCT
ejpam-6331	230	7	the	the	DET
ejpam-6331	230	8	proof	proof	NOUN
ejpam-6331	230	9	follows	follow	VERB
ejpam-6331	230	10	similarly	similarly	ADV
ejpam-6331	230	11	by	by	ADP
ejpam-6331	230	12	expanding	expand	VERB
ejpam-6331	230	13	the	the	DET
ejpam-6331	230	14	terms	term	NOUN
ejpam-6331	230	15	.	.	PUNCT
ejpam-6331	231	1	the	the	DET
ejpam-6331	231	2	non	non	ADJ
ejpam-6331	231	3	-	-	ADJ
ejpam-6331	231	4	membership	membership	ADJ
ejpam-6331	231	5	condition	condition	NOUN
ejpam-6331	231	6	is	be	AUX
ejpam-6331	231	7	analogous	analogous	ADJ
ejpam-6331	231	8	.	.	PUNCT
ejpam-6331	232	1	(	(	PUNCT
ejpam-6331	232	2	3	3	X
ejpam-6331	232	3	)	)	PUNCT
ejpam-6331	232	4	⇒	⇒	NOUN
ejpam-6331	232	5	(	(	PUNCT
ejpam-6331	232	6	1	1	X
ejpam-6331	232	7	)	)	PUNCT
ejpam-6331	232	8	assume	assume	VERB
ejpam-6331	232	9	that	that	SCONJ
ejpam-6331	232	10	c	c	PROPN
ejpam-6331	232	11	is	be	AUX
ejpam-6331	232	12	a	a	DET
ejpam-6331	232	13	cifb	cifb	NOUN
ejpam-6331	232	14	-	-	PUNCT
ejpam-6331	232	15	ideal	ideal	NOUN
ejpam-6331	232	16	.	.	PUNCT
ejpam-6331	233	1	we	we	PRON
ejpam-6331	233	2	show	show	VERB
ejpam-6331	233	3	it	it	PRON
ejpam-6331	233	4	is	be	AUX
ejpam-6331	233	5	a	a	DET
ejpam-6331	233	6	cif	cif	PROPN
ejpam-6331	233	7	-	-	PUNCT
ejpam-6331	233	8	ideal	ideal	NOUN
ejpam-6331	233	9	.	.	PUNCT
ejpam-6331	234	1	for	for	ADP
ejpam-6331	234	2	any	any	DET
ejpam-6331	234	3	⌜	⌜	PROPN
ejpam-6331	234	4	ϱ̃	ϱ̃	PROPN
ejpam-6331	234	5	⌝	⌝	PROPN
ejpam-6331	234	6	,	,	PUNCT
ejpam-6331	234	7	⌜	⌜	PROPN
ejpam-6331	234	8	ϑ̃	ϑ̃	PROPN
ejpam-6331	234	9	⌝	⌝	PROPN
ejpam-6331	234	10	,	,	PUNCT
ejpam-6331	234	11	⌜	⌜	PROPN
ejpam-6331	234	12	κ̃	κ̃	PROPN
ejpam-6331	234	13	⌝	⌝	PROPN
ejpam-6331	234	14	∈	∈	PROPN
ejpam-6331	234	15	x	x	X
ejpam-6331	234	16	,	,	PUNCT
ejpam-6331	234	17	by	by	ADP
ejpam-6331	234	18	definition	definition	NOUN
ejpam-6331	234	19	8	8	NUM
ejpam-6331	234	20	,	,	PUNCT
ejpam-6331	234	21	we	we	PRON
ejpam-6331	234	22	have	have	VERB
ejpam-6331	234	23	∅̃c(	∅̃c(	NOUN
ejpam-6331	234	24	⌜	⌜	NOUN
ejpam-6331	234	25	ϱ̃	ϱ̃	PROPN
ejpam-6331	234	26	⌝	⌝	PROPN
ejpam-6331	234	27	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	234	28	⌜	⌜	PROPN
ejpam-6331	234	29	ϱ̃	ϱ̃	PROPN
ejpam-6331	234	30	⌝	⌝	PROPN
ejpam-6331	234	31	)	)	PUNCT
ejpam-6331	234	32	≥	≥	NOUN
ejpam-6331	234	33	min{∅̃c((	min{∅̃c((	PROPN
ejpam-6331	234	34	⌜	⌜	PROPN
ejpam-6331	234	35	ϱ̃	ϱ̃	PROPN
ejpam-6331	234	36	⌝	⌝	PROPN
ejpam-6331	234	37	∗	∗	NOUN
ejpam-6331	234	38	⌜	⌜	PROPN
ejpam-6331	234	39	κ̃	κ̃	PROPN
ejpam-6331	234	40	⌝	⌝	PROPN
ejpam-6331	234	41	)	)	PUNCT
ejpam-6331	234	42	∗	∗	NOUN
ejpam-6331	234	43	⌜	⌜	PROPN
ejpam-6331	234	44	ϑ̃	ϑ̃	PROPN
ejpam-6331	234	45	⌝	⌝	PROPN
ejpam-6331	234	46	)eiω̃c((	)eiω̃c((	PROPN
ejpam-6331	234	47	⌜	⌜	PROPN
ejpam-6331	234	48	ϱ̃	ϱ̃	PROPN
ejpam-6331	234	49	⌝	⌝	PROPN
ejpam-6331	234	50	∗	∗	NOUN
ejpam-6331	234	51	⌜	⌜	PROPN
ejpam-6331	234	52	κ̃	κ̃	PROPN
ejpam-6331	234	53	⌝	⌝	PROPN
ejpam-6331	234	54	)∗	)∗	PROPN
ejpam-6331	234	55	⌜	⌜	PROPN
ejpam-6331	234	56	ϑ̃	ϑ̃	PROPN
ejpam-6331	234	57	⌝	⌝	PROPN
ejpam-6331	234	58	)	)	PUNCT
ejpam-6331	234	59	,	,	PUNCT
ejpam-6331	234	60	∅̃c(	∅̃c(	NOUN
ejpam-6331	234	61	⌜	⌜	SYM
ejpam-6331	234	62	ϑ̃	ϑ̃	PROPN
ejpam-6331	234	63	⌝	⌝	PROPN
ejpam-6331	234	64	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	234	65	⌜	⌜	PROPN
ejpam-6331	234	66	ϑ̃	ϑ̃	PROPN
ejpam-6331	234	67	⌝	⌝	PROPN
ejpam-6331	234	68	)	)	PUNCT
ejpam-6331	234	69	}	}	PUNCT
ejpam-6331	234	70	.	.	PUNCT
ejpam-6331	235	1	setting	set	VERB
ejpam-6331	235	2	⌜	⌜	PROPN
ejpam-6331	235	3	κ̃	κ̃	PROPN
ejpam-6331	235	4	⌝	⌝	PROPN
ejpam-6331	235	5	=	=	SYM
ejpam-6331	235	6	0	0	NUM
ejpam-6331	235	7	,	,	PUNCT
ejpam-6331	235	8	we	we	PRON
ejpam-6331	235	9	get	get	VERB
ejpam-6331	235	10	∅̃c(	∅̃c(	NOUN
ejpam-6331	235	11	⌜	⌜	NOUN
ejpam-6331	235	12	ϱ̃	ϱ̃	PROPN
ejpam-6331	235	13	⌝	⌝	PROPN
ejpam-6331	235	14	)eiω̃c(	)eiω̃c(	NOUN
ejpam-6331	235	15	⌜	⌜	PROPN
ejpam-6331	235	16	ϱ̃	ϱ̃	PROPN
ejpam-6331	235	17	⌝	⌝	PROPN
ejpam-6331	235	18	)	)	PUNCT
ejpam-6331	235	19	≥	≥	NOUN
ejpam-6331	235	20	min{∅̃c((	min{∅̃c((	PROPN
ejpam-6331	235	21	⌜	⌜	PROPN
ejpam-6331	235	22	ϱ̃	ϱ̃	PROPN
ejpam-6331	235	23	⌝	⌝	PROPN
ejpam-6331	235	24	∗	∗	NOUN
ejpam-6331	235	25	0	0	NUM
ejpam-6331	235	26	)	)	PUNCT
ejpam-6331	236	1	∗	∗	NOUN
ejpam-6331	236	2	⌜	⌜	PROPN
ejpam-6331	236	3	ϑ̃	ϑ̃	PROPN
ejpam-6331	236	4	⌝	⌝	PROPN
ejpam-6331	236	5	)eiω̃c((	)eiω̃c((	PROPN
ejpam-6331	236	6	⌜	⌜	PROPN
ejpam-6331	236	7	ϱ̃	ϱ̃	PROPN
ejpam-6331	236	8	⌝	⌝	PROPN
ejpam-6331	236	9	∗0)∗	∗0)∗	ADJ
ejpam-6331	236	10	⌜	⌜	PROPN
ejpam-6331	236	11	ϑ̃	ϑ̃	PROPN
ejpam-6331	236	12	⌝	⌝	PROPN
ejpam-6331	236	13	)	)	PUNCT
ejpam-6331	236	14	,	,	PUNCT
ejpam-6331	236	15	∅̃c(	∅̃c(	NOUN
ejpam-6331	236	16	⌜	⌜	SYM
ejpam-6331	236	17	ϑ̃	ϑ̃	PROPN
ejpam-6331	236	18	⌝	⌝	PROPN
ejpam-6331	236	19	)eiω̃c(	)eiω̃c(	PROPN
ejpam-6331	236	20	⌜	⌜	PROPN
ejpam-6331	236	21	ϑ̃	ϑ̃	PROPN
ejpam-6331	236	22	⌝	⌝	PROPN
ejpam-6331	236	23	)	)	PUNCT
ejpam-6331	236	24	}	}	PUNCT
ejpam-6331	236	25	.	.	PUNCT
ejpam-6331	237	1	this	this	PRON
ejpam-6331	237	2	is	be	AUX
ejpam-6331	237	3	the	the	DET
ejpam-6331	237	4	condition	condition	NOUN
ejpam-6331	237	5	for	for	ADP
ejpam-6331	237	6	cif	cif	PROPN
ejpam-6331	237	7	-	-	PUNCT
ejpam-6331	237	8	ideal	ideal	NOUN
ejpam-6331	237	9	.	.	PUNCT
ejpam-6331	238	1	the	the	DET
ejpam-6331	238	2	non	non	ADJ
ejpam-6331	238	3	-	-	ADJ
ejpam-6331	238	4	membership	membership	ADJ
ejpam-6331	238	5	condition	condition	NOUN
ejpam-6331	238	6	is	be	AUX
ejpam-6331	238	7	similarly	similarly	ADV
ejpam-6331	238	8	verified	verify	VERB
ejpam-6331	238	9	.	.	PUNCT
ejpam-6331	239	1	thus	thus	ADV
ejpam-6331	239	2	,	,	PUNCT
ejpam-6331	239	3	the	the	DET
ejpam-6331	239	4	three	three	NUM
ejpam-6331	239	5	conditions	condition	NOUN
ejpam-6331	239	6	are	be	AUX
ejpam-6331	239	7	equivalent	equivalent	ADJ
ejpam-6331	239	8	.	.	PUNCT
ejpam-6331	240	1	5	5	X
ejpam-6331	240	2	.	.	X
ejpam-6331	240	3	conclusion	conclusion	NOUN
ejpam-6331	240	4	in	in	ADP
ejpam-6331	240	5	this	this	DET
ejpam-6331	240	6	study	study	NOUN
ejpam-6331	240	7	,	,	PUNCT
ejpam-6331	240	8	we	we	PRON
ejpam-6331	240	9	established	establish	VERB
ejpam-6331	240	10	a	a	DET
ejpam-6331	240	11	comprehensive	comprehensive	ADJ
ejpam-6331	240	12	framework	framework	NOUN
ejpam-6331	240	13	connecting	connect	VERB
ejpam-6331	240	14	complex	complex	ADJ
ejpam-6331	240	15	intuitionistic	intuitionistic	ADJ
ejpam-6331	240	16	fuzzy	fuzzy	ADJ
ejpam-6331	240	17	ideals	ideal	NOUN
ejpam-6331	240	18	(	(	PUNCT
ejpam-6331	240	19	cif	cif	PROPN
ejpam-6331	240	20	-	-	PUNCT
ejpam-6331	240	21	ideals	ideal	NOUN
ejpam-6331	240	22	)	)	PUNCT
ejpam-6331	240	23	,	,	PUNCT
ejpam-6331	240	24	quasi	quasi	ADJ
ejpam-6331	240	25	-	-	ADJ
ejpam-6331	240	26	associative	associative	ADJ
ejpam-6331	240	27	ideals	ideal	NOUN
ejpam-6331	240	28	(	(	PUNCT
ejpam-6331	240	29	cifqa	cifqa	NOUN
ejpam-6331	240	30	-	-	PUNCT
ejpam-6331	240	31	ideals	ideal	NOUN
ejpam-6331	240	32	)	)	PUNCT
ejpam-6331	240	33	,	,	PUNCT
ejpam-6331	240	34	and	and	CCONJ
ejpam-6331	240	35	b	b	X
ejpam-6331	240	36	-	-	PUNCT
ejpam-6331	240	37	ideals	ideal	NOUN
ejpam-6331	240	38	(	(	PUNCT
ejpam-6331	240	39	cifb	cifb	NOUN
ejpam-6331	240	40	-	-	PUNCT
ejpam-6331	240	41	ideals	ideal	NOUN
ejpam-6331	240	42	)	)	PUNCT
ejpam-6331	240	43	within	within	ADP
ejpam-6331	240	44	bci	bci	NOUN
ejpam-6331	240	45	-	-	PUNCT
ejpam-6331	240	46	algebras	algebras	X
ejpam-6331	240	47	.	.	PUNCT
ejpam-6331	241	1	we	we	PRON
ejpam-6331	241	2	formally	formally	ADV
ejpam-6331	241	3	introduced	introduce	VERB
ejpam-6331	241	4	the	the	DET
ejpam-6331	241	5	notion	notion	NOUN
ejpam-6331	241	6	of	of	ADP
ejpam-6331	241	7	cifqa	cifqa	NOUN
ejpam-6331	241	8	-	-	PUNCT
ejpam-6331	241	9	ideals	ideal	NOUN
ejpam-6331	241	10	and	and	CCONJ
ejpam-6331	241	11	demonstrated	demonstrate	VERB
ejpam-6331	241	12	that	that	SCONJ
ejpam-6331	241	13	every	every	DET
ejpam-6331	241	14	cifqa	cifqa	NOUN
ejpam-6331	241	15	-	-	PUNCT
ejpam-6331	241	16	ideal	ideal	NOUN
ejpam-6331	241	17	is	be	AUX
ejpam-6331	241	18	inherently	inherently	ADV
ejpam-6331	241	19	a	a	DET
ejpam-6331	241	20	cif	cif	PROPN
ejpam-6331	241	21	-	-	PUNCT
ejpam-6331	241	22	ideal	ideal	NOUN
ejpam-6331	241	23	.	.	PUNCT
ejpam-6331	242	1	however	however	ADV
ejpam-6331	242	2	,	,	PUNCT
ejpam-6331	242	3	through	through	ADP
ejpam-6331	242	4	counterexamples	counterexample	NOUN
ejpam-6331	242	5	,	,	PUNCT
ejpam-6331	242	6	we	we	PRON
ejpam-6331	242	7	showed	show	VERB
ejpam-6331	242	8	that	that	SCONJ
ejpam-6331	242	9	the	the	DET
ejpam-6331	242	10	converse	converse	NOUN
ejpam-6331	242	11	does	do	AUX
ejpam-6331	242	12	not	not	PART
ejpam-6331	242	13	generally	generally	ADV
ejpam-6331	242	14	hold	hold	VERB
ejpam-6331	242	15	.	.	PUNCT
ejpam-6331	243	1	we	we	PRON
ejpam-6331	243	2	further	far	ADV
ejpam-6331	243	3	derived	derive	VERB
ejpam-6331	243	4	necessary	necessary	ADJ
ejpam-6331	243	5	and	and	CCONJ
ejpam-6331	243	6	sufficient	sufficient	ADJ
ejpam-6331	243	7	conditions	condition	NOUN
ejpam-6331	243	8	under	under	ADP
ejpam-6331	243	9	which	which	PRON
ejpam-6331	243	10	all	all	DET
ejpam-6331	243	11	three	three	NUM
ejpam-6331	243	12	classes	class	NOUN
ejpam-6331	243	13	of	of	ADP
ejpam-6331	243	14	ideals	ideal	NOUN
ejpam-6331	243	15	coincide	coincide	VERB
ejpam-6331	243	16	,	,	PUNCT
ejpam-6331	243	17	and	and	CCONJ
ejpam-6331	243	18	established	establish	VERB
ejpam-6331	243	19	that	that	SCONJ
ejpam-6331	243	20	these	these	DET
ejpam-6331	243	21	conditions	condition	NOUN
ejpam-6331	243	22	depend	depend	VERB
ejpam-6331	243	23	on	on	ADP
ejpam-6331	243	24	the	the	DET
ejpam-6331	243	25	quasi	quasi	NOUN
ejpam-6331	243	26	-	-	NOUN
ejpam-6331	243	27	associativity	associativity	NOUN
ejpam-6331	243	28	of	of	ADP
ejpam-6331	243	29	the	the	DET
ejpam-6331	243	30	underlying	underlie	VERB
ejpam-6331	243	31	algebraic	algebraic	ADJ
ejpam-6331	243	32	structure	structure	NOUN
ejpam-6331	243	33	.	.	PUNCT
ejpam-6331	244	1	these	these	DET
ejpam-6331	244	2	findings	finding	NOUN
ejpam-6331	244	3	reveal	reveal	VERB
ejpam-6331	244	4	a	a	DET
ejpam-6331	244	5	hierarchical	hierarchical	ADJ
ejpam-6331	244	6	lattice	lattice	NOUN
ejpam-6331	244	7	among	among	ADP
ejpam-6331	244	8	the	the	DET
ejpam-6331	244	9	ideals	ideal	NOUN
ejpam-6331	244	10	and	and	CCONJ
ejpam-6331	244	11	t.	t.	PROPN
ejpam-6331	244	12	ramesh	ramesh	PROPN
ejpam-6331	244	13	,	,	PUNCT
ejpam-6331	244	14	m.	m.	NOUN
ejpam-6331	244	15	balamurugan	balamurugan	PROPN
ejpam-6331	244	16	,	,	PUNCT
ejpam-6331	244	17	a.	a.	NOUN
ejpam-6331	244	18	iampan	iampan	PROPN
ejpam-6331	244	19	/	/	SYM
ejpam-6331	244	20	eur	eur	PROPN
ejpam-6331	244	21	.	.	PUNCT
ejpam-6331	245	1	j.	j.	PROPN
ejpam-6331	245	2	pure	pure	PROPN
ejpam-6331	245	3	appl	appl	PROPN
ejpam-6331	245	4	.	.	PROPN
ejpam-6331	245	5	math	math	PROPN
ejpam-6331	245	6	,	,	PUNCT
ejpam-6331	245	7	18	18	NUM
ejpam-6331	245	8	(	(	PUNCT
ejpam-6331	245	9	3	3	NUM
ejpam-6331	245	10	)	)	PUNCT
ejpam-6331	245	11	(	(	PUNCT
ejpam-6331	245	12	2025	2025	NUM
ejpam-6331	245	13	)	)	PUNCT
ejpam-6331	245	14	,	,	PUNCT
ejpam-6331	245	15	6331	6331	NUM
ejpam-6331	245	16	13	13	NUM
ejpam-6331	245	17	of	of	ADP
ejpam-6331	245	18	14	14	NUM
ejpam-6331	245	19	illustrate	illustrate	VERB
ejpam-6331	245	20	the	the	DET
ejpam-6331	245	21	bridging	bridging	ADJ
ejpam-6331	245	22	role	role	NOUN
ejpam-6331	245	23	of	of	ADP
ejpam-6331	245	24	cifqa	cifqa	NOUN
ejpam-6331	245	25	-	-	PUNCT
ejpam-6331	245	26	ideals	ideal	NOUN
ejpam-6331	245	27	between	between	ADP
ejpam-6331	245	28	general	general	ADJ
ejpam-6331	245	29	fuzzy	fuzzy	ADJ
ejpam-6331	245	30	ideals	ideal	NOUN
ejpam-6331	245	31	and	and	CCONJ
ejpam-6331	245	32	the	the	DET
ejpam-6331	245	33	more	more	ADV
ejpam-6331	245	34	restrictive	restrictive	ADJ
ejpam-6331	245	35	b	b	NOUN
ejpam-6331	245	36	-	-	PUNCT
ejpam-6331	245	37	ideals	ideal	NOUN
ejpam-6331	245	38	.	.	PUNCT
ejpam-6331	246	1	future	future	ADJ
ejpam-6331	246	2	research	research	NOUN
ejpam-6331	246	3	could	could	AUX
ejpam-6331	246	4	explore	explore	VERB
ejpam-6331	246	5	extensions	extension	NOUN
ejpam-6331	246	6	of	of	ADP
ejpam-6331	246	7	these	these	DET
ejpam-6331	246	8	ideal	ideal	ADJ
ejpam-6331	246	9	structures	structure	NOUN
ejpam-6331	246	10	to	to	ADP
ejpam-6331	246	11	more	more	ADV
ejpam-6331	246	12	generalized	generalized	ADJ
ejpam-6331	246	13	algebraic	algebraic	ADJ
ejpam-6331	246	14	systems	system	NOUN
ejpam-6331	246	15	such	such	ADJ
ejpam-6331	246	16	as	as	ADP
ejpam-6331	246	17	bci	bci	NOUN
ejpam-6331	246	18	-	-	PUNCT
ejpam-6331	246	19	semigroups	semigroup	NOUN
ejpam-6331	246	20	,	,	PUNCT
ejpam-6331	246	21	n	n	CCONJ
ejpam-6331	246	22	-	-	PUNCT
ejpam-6331	246	23	ary	ary	PROPN
ejpam-6331	246	24	bci	bci	NOUN
ejpam-6331	246	25	-	-	PUNCT
ejpam-6331	246	26	algebras	algebra	NOUN
ejpam-6331	246	27	,	,	PUNCT
ejpam-6331	246	28	or	or	CCONJ
ejpam-6331	246	29	their	their	PRON
ejpam-6331	246	30	neutrosophic	neutrosophic	ADJ
ejpam-6331	246	31	and	and	CCONJ
ejpam-6331	246	32	soft	soft	ADJ
ejpam-6331	246	33	set	set	ADJ
ejpam-6331	246	34	analogues	analogue	NOUN
ejpam-6331	246	35	.	.	PUNCT
ejpam-6331	247	1	additionally	additionally	ADV
ejpam-6331	247	2	,	,	PUNCT
ejpam-6331	247	3	applications	application	NOUN
ejpam-6331	247	4	in	in	ADP
ejpam-6331	247	5	decision	decision	NOUN
ejpam-6331	247	6	support	support	NOUN
ejpam-6331	247	7	systems	system	NOUN
ejpam-6331	247	8	,	,	PUNCT
ejpam-6331	247	9	logic	logic	NOUN
ejpam-6331	247	10	programming	programming	NOUN
ejpam-6331	247	11	,	,	PUNCT
ejpam-6331	247	12	and	and	CCONJ
ejpam-6331	247	13	computational	computational	ADJ
ejpam-6331	247	14	models	model	NOUN
ejpam-6331	247	15	under	under	ADP
ejpam-6331	247	16	hybrid	hybrid	ADJ
ejpam-6331	247	17	uncertainty	uncertainty	NOUN
ejpam-6331	247	18	could	could	AUX
ejpam-6331	247	19	benefit	benefit	VERB
ejpam-6331	247	20	from	from	ADP
ejpam-6331	247	21	the	the	DET
ejpam-6331	247	22	theoretical	theoretical	ADJ
ejpam-6331	247	23	foundations	foundation	NOUN
ejpam-6331	247	24	laid	lay	VERB
ejpam-6331	247	25	in	in	ADP
ejpam-6331	247	26	this	this	DET
ejpam-6331	247	27	work	work	NOUN
ejpam-6331	247	28	.	.	PUNCT
ejpam-6331	248	1	acknowledgements	acknowledgement	NOUN
ejpam-6331	248	2	this	this	DET
ejpam-6331	248	3	research	research	NOUN
ejpam-6331	248	4	was	be	AUX
ejpam-6331	248	5	supported	support	VERB
ejpam-6331	248	6	by	by	ADP
ejpam-6331	248	7	university	university	NOUN
ejpam-6331	248	8	of	of	ADP
ejpam-6331	248	9	phayao	phayao	NOUN
ejpam-6331	248	10	and	and	CCONJ
ejpam-6331	248	11	thailand	thailand	PROPN
ejpam-6331	248	12	science	science	PROPN
ejpam-6331	248	13	research	research	PROPN
ejpam-6331	248	14	and	and	CCONJ
ejpam-6331	248	15	innovation	innovation	NOUN
ejpam-6331	248	16	fund	fund	NOUN
ejpam-6331	248	17	(	(	PUNCT
ejpam-6331	248	18	fundamental	fundamental	ADJ
ejpam-6331	248	19	fund	fund	NOUN
ejpam-6331	248	20	2025	2025	NUM
ejpam-6331	248	21	,	,	PUNCT
ejpam-6331	248	22	grant	grant	VERB
ejpam-6331	248	23	no	no	NOUN
ejpam-6331	248	24	.	.	PROPN
ejpam-6331	249	1	5027/2567	5027/2567	NUM
ejpam-6331	249	2	)	)	PUNCT
ejpam-6331	249	3	.	.	PUNCT
ejpam-6331	250	1	references	reference	NOUN
ejpam-6331	250	2	[	[	X
ejpam-6331	250	3	1	1	NUM
ejpam-6331	250	4	]	]	PUNCT
ejpam-6331	250	5	l.	l.	PROPN
ejpam-6331	250	6	a.	a.	PROPN
ejpam-6331	250	7	zadeh	zadeh	PROPN
ejpam-6331	250	8	.	.	PUNCT
ejpam-6331	251	1	fuzzy	fuzzy	ADJ
ejpam-6331	251	2	sets	set	NOUN
ejpam-6331	251	3	.	.	PUNCT
ejpam-6331	252	1	information	information	NOUN
ejpam-6331	252	2	and	and	CCONJ
ejpam-6331	252	3	control	control	NOUN
ejpam-6331	252	4	,	,	PUNCT
ejpam-6331	252	5	8(3):338–353	8(3):338–353	NUM
ejpam-6331	252	6	,	,	PUNCT
ejpam-6331	252	7	1965	1965	NUM
ejpam-6331	252	8	.	.	PUNCT
ejpam-6331	253	1	[	[	X
ejpam-6331	253	2	2	2	NUM
ejpam-6331	253	3	]	]	PUNCT
ejpam-6331	253	4	a.	a.	NOUN
ejpam-6331	253	5	rosenfeld	rosenfeld	PROPN
ejpam-6331	253	6	.	.	PUNCT
ejpam-6331	254	1	fuzzy	fuzzy	ADJ
ejpam-6331	254	2	groups	group	NOUN
ejpam-6331	254	3	.	.	PUNCT
ejpam-6331	255	1	journal	journal	PROPN
ejpam-6331	255	2	of	of	ADP
ejpam-6331	255	3	mathematical	mathematical	ADJ
ejpam-6331	255	4	analysis	analysis	NOUN
ejpam-6331	255	5	and	and	CCONJ
ejpam-6331	255	6	applications	application	NOUN
ejpam-6331	255	7	,	,	PUNCT
ejpam-6331	255	8	35:512–517	35:512–517	PROPN
ejpam-6331	255	9	,	,	PUNCT
ejpam-6331	255	10	1971	1971	NUM
ejpam-6331	255	11	.	.	PUNCT
ejpam-6331	256	1	[	[	X
ejpam-6331	256	2	3	3	NUM
ejpam-6331	256	3	]	]	X
ejpam-6331	256	4	y.	y.	PROPN
ejpam-6331	256	5	imai	imai	PROPN
ejpam-6331	256	6	and	and	CCONJ
ejpam-6331	256	7	k.	k.	PROPN
ejpam-6331	256	8	iséki	iséki	PROPN
ejpam-6331	256	9	.	.	PROPN
ejpam-6331	257	1	on	on	ADP
ejpam-6331	257	2	axiom	axiom	NOUN
ejpam-6331	257	3	systems	system	NOUN
ejpam-6331	257	4	of	of	ADP
ejpam-6331	257	5	propositional	propositional	ADJ
ejpam-6331	257	6	calculi	calculi	PROPN
ejpam-6331	257	7	,	,	PUNCT
ejpam-6331	257	8	xiv	xiv	PROPN
ejpam-6331	257	9	.	.	PUNCT
ejpam-6331	258	1	proceedings	proceeding	NOUN
ejpam-6331	258	2	of	of	ADP
ejpam-6331	258	3	the	the	DET
ejpam-6331	258	4	japan	japan	PROPN
ejpam-6331	258	5	academy	academy	PROPN
ejpam-6331	258	6	,	,	PUNCT
ejpam-6331	258	7	42:19–21	42:19–21	NUM
ejpam-6331	258	8	,	,	PUNCT
ejpam-6331	258	9	1966	1966	NUM
ejpam-6331	258	10	.	.	PUNCT
ejpam-6331	259	1	[	[	X
ejpam-6331	259	2	4	4	X
ejpam-6331	259	3	]	]	PUNCT
ejpam-6331	259	4	k.	k.	PROPN
ejpam-6331	259	5	iséki	iséki	PROPN
ejpam-6331	259	6	.	.	PUNCT
ejpam-6331	260	1	an	an	DET
ejpam-6331	260	2	algebra	algebra	NOUN
ejpam-6331	260	3	related	relate	VERB
ejpam-6331	260	4	with	with	ADP
ejpam-6331	260	5	a	a	DET
ejpam-6331	260	6	propositional	propositional	ADJ
ejpam-6331	260	7	calculus	calculus	NOUN
ejpam-6331	260	8	.	.	PUNCT
ejpam-6331	261	1	proceedings	proceeding	NOUN
ejpam-6331	261	2	of	of	ADP
ejpam-6331	261	3	the	the	DET
ejpam-6331	261	4	japan	japan	PROPN
ejpam-6331	261	5	academy	academy	PROPN
ejpam-6331	261	6	,	,	PUNCT
ejpam-6331	261	7	42:26–29	42:26–29	PROPN
ejpam-6331	261	8	,	,	PUNCT
ejpam-6331	261	9	1966	1966	NUM
ejpam-6331	261	10	.	.	PUNCT
ejpam-6331	262	1	[	[	X
ejpam-6331	262	2	5	5	X
ejpam-6331	262	3	]	]	PUNCT
ejpam-6331	262	4	k.	k.	PROPN
ejpam-6331	262	5	iséki	iséki	PROPN
ejpam-6331	262	6	and	and	CCONJ
ejpam-6331	262	7	s.	s.	PROPN
ejpam-6331	262	8	tanaka	tanaka	PROPN
ejpam-6331	262	9	.	.	PUNCT
ejpam-6331	263	1	an	an	DET
ejpam-6331	263	2	introduction	introduction	NOUN
ejpam-6331	263	3	to	to	ADP
ejpam-6331	263	4	the	the	DET
ejpam-6331	263	5	theory	theory	NOUN
ejpam-6331	263	6	of	of	ADP
ejpam-6331	263	7	bck	bck	PROPN
ejpam-6331	263	8	-	-	PUNCT
ejpam-6331	263	9	algebras	algebras	PROPN
ejpam-6331	263	10	.	.	PUNCT
ejpam-6331	264	1	mathematica	mathematica	PROPN
ejpam-6331	264	2	japonica	japonica	PROPN
ejpam-6331	264	3	,	,	PUNCT
ejpam-6331	264	4	3:1–26	3:1–26	NUM
ejpam-6331	264	5	,	,	PUNCT
ejpam-6331	264	6	1978	1978	NUM
ejpam-6331	264	7	.	.	PUNCT
ejpam-6331	265	1	[	[	X
ejpam-6331	265	2	6	6	NUM
ejpam-6331	265	3	]	]	PUNCT
ejpam-6331	265	4	z.	z.	PROPN
ejpam-6331	265	5	yue	yue	PROPN
ejpam-6331	265	6	and	and	CCONJ
ejpam-6331	265	7	x.	x.	PROPN
ejpam-6331	265	8	h.	h.	PROPN
ejpam-6331	265	9	zhang	zhang	PROPN
ejpam-6331	265	10	.	.	PUNCT
ejpam-6331	266	1	quasi	quasi	ADJ
ejpam-6331	266	2	-	-	ADJ
ejpam-6331	266	3	associative	associative	ADJ
ejpam-6331	266	4	ideals	ideal	NOUN
ejpam-6331	266	5	in	in	ADP
ejpam-6331	266	6	bci	bci	NOUN
ejpam-6331	266	7	-	-	PUNCT
ejpam-6331	266	8	algebras	algebras	X
ejpam-6331	266	9	.	.	PUNCT
ejpam-6331	267	1	select	select	ADJ
ejpam-6331	267	2	papers	paper	NOUN
ejpam-6331	267	3	on	on	ADP
ejpam-6331	267	4	bck	bck	PROPN
ejpam-6331	267	5	and	and	CCONJ
ejpam-6331	267	6	bci	bci	NOUN
ejpam-6331	267	7	-	-	PUNCT
ejpam-6331	267	8	algebras	algebra	NOUN
ejpam-6331	267	9	,	,	PUNCT
ejpam-6331	267	10	1:338–353	1:338–353	NUM
ejpam-6331	267	11	,	,	PUNCT
ejpam-6331	267	12	1992	1992	NUM
ejpam-6331	267	13	.	.	PUNCT
ejpam-6331	268	1	[	[	X
ejpam-6331	268	2	7	7	X
ejpam-6331	268	3	]	]	X
ejpam-6331	268	4	o.	o.	NOUN
ejpam-6331	268	5	g.	g.	PROPN
ejpam-6331	269	1	xi	xi	PROPN
ejpam-6331	269	2	.	.	PUNCT
ejpam-6331	270	1	fuzzy	fuzzy	ADJ
ejpam-6331	270	2	bck	bck	PROPN
ejpam-6331	270	3	-	-	PUNCT
ejpam-6331	270	4	algebras	algebras	PROPN
ejpam-6331	270	5	.	.	PUNCT
ejpam-6331	271	1	mathematica	mathematica	PROPN
ejpam-6331	271	2	japonica	japonica	PROPN
ejpam-6331	271	3	,	,	PUNCT
ejpam-6331	271	4	36(5):935–942	36(5):935–942	NUM
ejpam-6331	271	5	,	,	PUNCT
ejpam-6331	271	6	1991	1991	NUM
ejpam-6331	271	7	.	.	PUNCT
ejpam-6331	272	1	[	[	X
ejpam-6331	272	2	8	8	NUM
ejpam-6331	272	3	]	]	X
ejpam-6331	272	4	b.	b.	PROPN
ejpam-6331	272	5	b.	b.	PROPN
ejpam-6331	272	6	ahmad	ahmad	PROPN
ejpam-6331	272	7	.	.	PUNCT
ejpam-6331	273	1	fuzzy	fuzzy	PROPN
ejpam-6331	273	2	bci	bci	NOUN
ejpam-6331	273	3	-	-	PUNCT
ejpam-6331	273	4	algebras	algebras	X
ejpam-6331	273	5	.	.	PUNCT
ejpam-6331	274	1	the	the	DET
ejpam-6331	274	2	journal	journal	NOUN
ejpam-6331	274	3	of	of	ADP
ejpam-6331	274	4	fuzzy	fuzzy	ADJ
ejpam-6331	274	5	mathematics	mathematic	NOUN
ejpam-6331	274	6	,	,	PUNCT
ejpam-6331	274	7	1:445–452	1:445–452	NOUN
ejpam-6331	274	8	,	,	PUNCT
ejpam-6331	274	9	1993	1993	NUM
ejpam-6331	274	10	.	.	PUNCT
ejpam-6331	275	1	[	[	X
ejpam-6331	275	2	9	9	NUM
ejpam-6331	275	3	]	]	X
ejpam-6331	275	4	y.	y.	PROPN
ejpam-6331	275	5	b.	b.	PROPN
ejpam-6331	275	6	jun	jun	PROPN
ejpam-6331	275	7	and	and	CCONJ
ejpam-6331	275	8	k.	k.	PROPN
ejpam-6331	275	9	h.	h.	PROPN
ejpam-6331	275	10	kim	kim	PROPN
ejpam-6331	275	11	.	.	PUNCT
ejpam-6331	276	1	intuitionistic	intuitionistic	ADJ
ejpam-6331	276	2	fuzzy	fuzzy	ADJ
ejpam-6331	276	3	ideals	ideal	NOUN
ejpam-6331	276	4	of	of	ADP
ejpam-6331	276	5	bck	bck	NOUN
ejpam-6331	276	6	-	-	PUNCT
ejpam-6331	276	7	algebras	algebras	PROPN
ejpam-6331	276	8	.	.	PUNCT
ejpam-6331	277	1	international	international	ADJ
ejpam-6331	277	2	journal	journal	PROPN
ejpam-6331	277	3	of	of	ADP
ejpam-6331	277	4	mathematics	mathematics	PROPN
ejpam-6331	277	5	and	and	CCONJ
ejpam-6331	277	6	mathematical	mathematical	ADJ
ejpam-6331	277	7	sciences	science	NOUN
ejpam-6331	277	8	,	,	PUNCT
ejpam-6331	277	9	24:839–849	24:839–849	NUM
ejpam-6331	277	10	,	,	PUNCT
ejpam-6331	277	11	2000	2000	NUM
ejpam-6331	277	12	.	.	PUNCT
ejpam-6331	278	1	[	[	X
ejpam-6331	278	2	10	10	NUM
ejpam-6331	278	3	]	]	X
ejpam-6331	278	4	c.	c.	PROPN
ejpam-6331	278	5	lele	lele	PROPN
ejpam-6331	278	6	and	and	CCONJ
ejpam-6331	278	7	s.	s.	PROPN
ejpam-6331	278	8	moutari	moutari	PROPN
ejpam-6331	278	9	.	.	PUNCT
ejpam-6331	279	1	on	on	ADP
ejpam-6331	279	2	n	n	CCONJ
ejpam-6331	279	3	-	-	ADJ
ejpam-6331	279	4	fold	fold	ADJ
ejpam-6331	279	5	quasi	quasi	ADJ
ejpam-6331	279	6	-	-	ADJ
ejpam-6331	279	7	associative	associative	ADJ
ejpam-6331	279	8	ideals	ideal	NOUN
ejpam-6331	279	9	in	in	ADP
ejpam-6331	279	10	bci	bci	NOUN
ejpam-6331	279	11	-	-	PUNCT
ejpam-6331	279	12	algebras	algebras	PROPN
ejpam-6331	279	13	.	.	PUNCT
ejpam-6331	279	14	samsa	samsa	PROPN
ejpam-6331	279	15	journal	journal	PROPN
ejpam-6331	279	16	of	of	ADP
ejpam-6331	279	17	pure	pure	ADJ
ejpam-6331	279	18	and	and	CCONJ
ejpam-6331	279	19	applied	applied	ADJ
ejpam-6331	279	20	mathematics	mathematic	NOUN
ejpam-6331	279	21	,	,	PUNCT
ejpam-6331	279	22	2(1):1–12	2(1):1–12	PROPN
ejpam-6331	279	23	,	,	PUNCT
ejpam-6331	279	24	2007	2007	NUM
ejpam-6331	279	25	.	.	PUNCT
ejpam-6331	280	1	[	[	X
ejpam-6331	280	2	11	11	NUM
ejpam-6331	280	3	]	]	PUNCT
ejpam-6331	280	4	k.	k.	PROPN
ejpam-6331	280	5	t.	t.	PROPN
ejpam-6331	280	6	atanassov	atanassov	PROPN
ejpam-6331	280	7	.	.	PUNCT
ejpam-6331	281	1	intuitionistic	intuitionistic	ADJ
ejpam-6331	281	2	fuzzy	fuzzy	ADJ
ejpam-6331	281	3	sets	set	NOUN
ejpam-6331	281	4	.	.	PUNCT
ejpam-6331	282	1	fuzzy	fuzzy	ADJ
ejpam-6331	282	2	sets	set	NOUN
ejpam-6331	282	3	and	and	CCONJ
ejpam-6331	282	4	systems	system	NOUN
ejpam-6331	282	5	,	,	PUNCT
ejpam-6331	282	6	20(1):87–96	20(1):87–96	NUM
ejpam-6331	282	7	,	,	PUNCT
ejpam-6331	282	8	1986	1986	NUM
ejpam-6331	282	9	.	.	PUNCT
ejpam-6331	283	1	[	[	X
ejpam-6331	283	2	12	12	NUM
ejpam-6331	283	3	]	]	X
ejpam-6331	283	4	y.	y.	PROPN
ejpam-6331	283	5	b.	b.	PROPN
ejpam-6331	283	6	jun	jun	PROPN
ejpam-6331	283	7	and	and	CCONJ
ejpam-6331	283	8	s.	s.	PROPN
ejpam-6331	283	9	z.	z.	PROPN
ejpam-6331	283	10	song	song	PROPN
ejpam-6331	283	11	.	.	PUNCT
ejpam-6331	284	1	falling	fall	VERB
ejpam-6331	284	2	fuzzy	fuzzy	ADJ
ejpam-6331	284	3	quasi	quasi	ADJ
ejpam-6331	284	4	-	-	ADJ
ejpam-6331	284	5	associative	associative	ADJ
ejpam-6331	284	6	ideals	ideal	NOUN
ejpam-6331	284	7	of	of	ADP
ejpam-6331	284	8	bci	bci	NOUN
ejpam-6331	284	9	-	-	PUNCT
ejpam-6331	284	10	algebras	algebra	NOUN
ejpam-6331	284	11	.	.	PUNCT
ejpam-6331	285	1	filomat	filomat	PROPN
ejpam-6331	285	2	,	,	PUNCT
ejpam-6331	285	3	26(4):649–656	26(4):649–656	NUM
ejpam-6331	285	4	,	,	PUNCT
ejpam-6331	285	5	2012	2012	NUM
ejpam-6331	285	6	.	.	PUNCT
ejpam-6331	286	1	[	[	X
ejpam-6331	286	2	13	13	NUM
ejpam-6331	286	3	]	]	X
ejpam-6331	286	4	d.	d.	PROPN
ejpam-6331	286	5	ramot	ramot	PROPN
ejpam-6331	286	6	,	,	PUNCT
ejpam-6331	286	7	m.	m.	NOUN
ejpam-6331	286	8	friedman	friedman	PROPN
ejpam-6331	286	9	,	,	PUNCT
ejpam-6331	286	10	g.	g.	PROPN
ejpam-6331	286	11	langholz	langholz	PROPN
ejpam-6331	286	12	,	,	PUNCT
ejpam-6331	286	13	and	and	CCONJ
ejpam-6331	286	14	a.	a.	NOUN
ejpam-6331	286	15	kandel	kandel	PROPN
ejpam-6331	286	16	.	.	PUNCT
ejpam-6331	287	1	complex	complex	ADJ
ejpam-6331	287	2	fuzzy	fuzzy	ADJ
ejpam-6331	287	3	logic	logic	NOUN
ejpam-6331	287	4	.	.	PUNCT
ejpam-6331	288	1	ieee	ieee	NOUN
ejpam-6331	288	2	transactions	transaction	NOUN
ejpam-6331	288	3	on	on	ADP
ejpam-6331	288	4	fuzzy	fuzzy	ADJ
ejpam-6331	288	5	systems	system	NOUN
ejpam-6331	288	6	,	,	PUNCT
ejpam-6331	288	7	11(4):450–461	11(4):450–461	NUM
ejpam-6331	288	8	,	,	PUNCT
ejpam-6331	288	9	2003	2003	NUM
ejpam-6331	288	10	.	.	PUNCT
ejpam-6331	289	1	[	[	X
ejpam-6331	289	2	14	14	NUM
ejpam-6331	289	3	]	]	X
ejpam-6331	289	4	d.	d.	PROPN
ejpam-6331	289	5	ramot	ramot	PROPN
ejpam-6331	289	6	,	,	PUNCT
ejpam-6331	289	7	r.	r.	PROPN
ejpam-6331	289	8	milo	milo	PROPN
ejpam-6331	289	9	,	,	PUNCT
ejpam-6331	289	10	m.	m.	NOUN
ejpam-6331	289	11	friedman	friedman	PROPN
ejpam-6331	289	12	,	,	PUNCT
ejpam-6331	289	13	and	and	CCONJ
ejpam-6331	289	14	a.	a.	NOUN
ejpam-6331	289	15	kandel	kandel	PROPN
ejpam-6331	289	16	.	.	PUNCT
ejpam-6331	290	1	complex	complex	ADJ
ejpam-6331	290	2	fuzzy	fuzzy	ADJ
ejpam-6331	290	3	sets	set	NOUN
ejpam-6331	290	4	.	.	PUNCT
ejpam-6331	291	1	ieee	ieee	NOUN
ejpam-6331	291	2	transactions	transaction	NOUN
ejpam-6331	291	3	on	on	ADP
ejpam-6331	291	4	fuzzy	fuzzy	ADJ
ejpam-6331	291	5	systems	system	NOUN
ejpam-6331	291	6	,	,	PUNCT
ejpam-6331	291	7	10(2):171–186	10(2):171–186	NUM
ejpam-6331	291	8	,	,	PUNCT
ejpam-6331	291	9	2002	2002	NUM
ejpam-6331	291	10	.	.	PUNCT
ejpam-6331	292	1	[	[	X
ejpam-6331	292	2	15	15	NUM
ejpam-6331	292	3	]	]	X
ejpam-6331	292	4	a.	a.	PROPN
ejpam-6331	292	5	al	al	PROPN
ejpam-6331	292	6	-	-	PUNCT
ejpam-6331	292	7	masarwah	masarwah	PROPN
ejpam-6331	292	8	,	,	PUNCT
ejpam-6331	292	9	m.	m.	NOUN
ejpam-6331	292	10	balamurugan	balamurugan	NOUN
ejpam-6331	292	11	,	,	PUNCT
ejpam-6331	292	12	t.	t.	PROPN
ejpam-6331	292	13	ramesh	ramesh	PROPN
ejpam-6331	292	14	,	,	PUNCT
ejpam-6331	292	15	m.	m.	NOUN
ejpam-6331	292	16	abuqamar	abuqamar	PROPN
ejpam-6331	292	17	,	,	PUNCT
ejpam-6331	292	18	and	and	CCONJ
ejpam-6331	292	19	m.	m.	NOUN
ejpam-6331	292	20	a.	a.	NOUN
ejpam-6331	292	21	alshayea	alshayea	PROPN
ejpam-6331	292	22	.	.	PUNCT
ejpam-6331	293	1	an	an	DET
ejpam-6331	293	2	investigation	investigation	NOUN
ejpam-6331	293	3	of	of	ADP
ejpam-6331	293	4	complex	complex	ADJ
ejpam-6331	293	5	linear	linear	ADJ
ejpam-6331	293	6	diophantine	diophantine	VERB
ejpam-6331	293	7	fuzzy	fuzzy	ADJ
ejpam-6331	293	8	ideals	ideal	NOUN
ejpam-6331	293	9	in	in	ADP
ejpam-6331	293	10	bck	bck	NOUN
ejpam-6331	293	11	-	-	PUNCT
ejpam-6331	293	12	algebras	algebras	PROPN
ejpam-6331	293	13	.	.	PUNCT
ejpam-6331	294	1	international	international	ADJ
ejpam-6331	294	2	journal	journal	PROPN
ejpam-6331	294	3	of	of	ADP
ejpam-6331	294	4	neutrosophic	neutrosophic	ADJ
ejpam-6331	294	5	science	science	NOUN
ejpam-6331	294	6	,	,	PUNCT
ejpam-6331	294	7	26(3):26–48	26(3):26–48	NUM
ejpam-6331	294	8	,	,	PUNCT
ejpam-6331	294	9	2025	2025	NUM
ejpam-6331	294	10	.	.	PUNCT
ejpam-6331	295	1	t.	t.	PROPN
ejpam-6331	295	2	ramesh	ramesh	PROPN
ejpam-6331	295	3	,	,	PUNCT
ejpam-6331	295	4	m.	m.	NOUN
ejpam-6331	295	5	balamurugan	balamurugan	PROPN
ejpam-6331	295	6	,	,	PUNCT
ejpam-6331	295	7	a.	a.	NOUN
ejpam-6331	295	8	iampan	iampan	PROPN
ejpam-6331	295	9	/	/	SYM
ejpam-6331	295	10	eur	eur	PROPN
ejpam-6331	295	11	.	.	PUNCT
ejpam-6331	296	1	j.	j.	PROPN
ejpam-6331	296	2	pure	pure	PROPN
ejpam-6331	296	3	appl	appl	PROPN
ejpam-6331	296	4	.	.	PROPN
ejpam-6331	296	5	math	math	PROPN
ejpam-6331	296	6	,	,	PUNCT
ejpam-6331	296	7	18	18	NUM
ejpam-6331	296	8	(	(	PUNCT
ejpam-6331	296	9	3	3	NUM
ejpam-6331	296	10	)	)	PUNCT
ejpam-6331	296	11	(	(	PUNCT
ejpam-6331	296	12	2025	2025	NUM
ejpam-6331	296	13	)	)	PUNCT
ejpam-6331	296	14	,	,	PUNCT
ejpam-6331	296	15	6331	6331	NUM
ejpam-6331	296	16	14	14	NUM
ejpam-6331	296	17	of	of	ADP
ejpam-6331	296	18	14	14	NUM
ejpam-6331	296	19	[	[	SYM
ejpam-6331	296	20	16	16	NUM
ejpam-6331	296	21	]	]	PUNCT
ejpam-6331	296	22	m.	m.	NOUN
ejpam-6331	296	23	deepika	deepika	PROPN
ejpam-6331	296	24	,	,	PUNCT
ejpam-6331	296	25	b.	b.	PROPN
ejpam-6331	296	26	elavarasan	elavarasan	PROPN
ejpam-6331	296	27	,	,	PUNCT
ejpam-6331	296	28	and	and	CCONJ
ejpam-6331	296	29	j.	j.	PROPN
ejpam-6331	296	30	catherine	catherine	PROPN
ejpam-6331	296	31	grace	grace	PROPN
ejpam-6331	296	32	john	john	PROPN
ejpam-6331	296	33	.	.	PUNCT
ejpam-6331	297	1	hybrid	hybrid	ADJ
ejpam-6331	297	2	quasi	quasi	NOUN
ejpam-6331	297	3	-	-	NOUN
ejpam-6331	297	4	ideals	ideal	NOUN
ejpam-6331	297	5	and	and	CCONJ
ejpam-6331	297	6	hybrid	hybrid	ADJ
ejpam-6331	297	7	a	a	DET
ejpam-6331	297	8	-	-	PUNCT
ejpam-6331	297	9	ideals	ideal	NOUN
ejpam-6331	297	10	in	in	ADP
ejpam-6331	297	11	ternary	ternary	ADJ
ejpam-6331	297	12	semigroups	semigroup	NOUN
ejpam-6331	297	13	.	.	PUNCT
ejpam-6331	298	1	songklanakarin	songklanakarin	PROPN
ejpam-6331	298	2	journal	journal	PROPN
ejpam-6331	298	3	of	of	ADP
ejpam-6331	298	4	science	science	NOUN
ejpam-6331	298	5	and	and	CCONJ
ejpam-6331	298	6	technology	technology	NOUN
ejpam-6331	298	7	,	,	PUNCT
ejpam-6331	298	8	46(1):16–23	46(1):16–23	NUM
ejpam-6331	298	9	,	,	PUNCT
ejpam-6331	298	10	2024	2024	NUM
ejpam-6331	298	11	.	.	PUNCT
ejpam-6331	299	1	[	[	X
ejpam-6331	299	2	17	17	NUM
ejpam-6331	299	3	]	]	PUNCT
ejpam-6331	299	4	m.	m.	NOUN
ejpam-6331	299	5	balamurugan	balamurugan	NOUN
ejpam-6331	299	6	,	,	PUNCT
ejpam-6331	299	7	t.	t.	PROPN
ejpam-6331	299	8	ramesh	ramesh	PROPN
ejpam-6331	299	9	,	,	PUNCT
ejpam-6331	299	10	a.	a.	PROPN
ejpam-6331	299	11	al	al	PROPN
ejpam-6331	299	12	-	-	PROPN
ejpam-6331	299	13	masarwah	masarwah	PROPN
ejpam-6331	299	14	,	,	PUNCT
ejpam-6331	299	15	and	and	CCONJ
ejpam-6331	299	16	k.	k.	PROPN
ejpam-6331	299	17	alsager	alsager	PROPN
ejpam-6331	299	18	.	.	PUNCT
ejpam-6331	300	1	new	new	ADJ
ejpam-6331	300	2	approach	approach	NOUN
ejpam-6331	300	3	of	of	ADP
ejpam-6331	300	4	complex	complex	ADJ
ejpam-6331	300	5	fuzzy	fuzzy	ADJ
ejpam-6331	300	6	ideals	ideal	NOUN
ejpam-6331	300	7	in	in	ADP
ejpam-6331	300	8	bck	bck	PROPN
ejpam-6331	300	9	/	/	SYM
ejpam-6331	300	10	bci	bci	NOUN
ejpam-6331	300	11	-	-	PUNCT
ejpam-6331	300	12	algebras	algebra	NOUN
ejpam-6331	300	13	.	.	PUNCT
ejpam-6331	301	1	mathematics	mathematic	NOUN
ejpam-6331	301	2	,	,	PUNCT
ejpam-6331	301	3	12(10):1583	12(10):1583	NUM
ejpam-6331	301	4	,	,	PUNCT
ejpam-6331	301	5	2024	2024	NUM
ejpam-6331	301	6	.	.	PUNCT
ejpam-6331	302	1	[	[	X
ejpam-6331	302	2	18	18	NUM
ejpam-6331	302	3	]	]	PUNCT
ejpam-6331	302	4	a.	a.	PROPN
ejpam-6331	302	5	s.	s.	PROPN
ejpam-6331	302	6	alkouri	alkouri	PROPN
ejpam-6331	302	7	and	and	CCONJ
ejpam-6331	302	8	a.	a.	PROPN
ejpam-6331	302	9	r.	r.	PROPN
ejpam-6331	302	10	salleh	salleh	PROPN
ejpam-6331	302	11	.	.	PUNCT
ejpam-6331	303	1	complex	complex	ADJ
ejpam-6331	303	2	intuitionistic	intuitionistic	ADJ
ejpam-6331	303	3	fuzzy	fuzzy	ADJ
ejpam-6331	303	4	sets	set	NOUN
ejpam-6331	303	5	.	.	PUNCT
ejpam-6331	304	1	in	in	ADP
ejpam-6331	304	2	aip	aip	PROPN
ejpam-6331	304	3	conference	conference	NOUN
ejpam-6331	304	4	proceedings	proceeding	NOUN
ejpam-6331	304	5	,	,	PUNCT
ejpam-6331	304	6	volume	volume	NOUN
ejpam-6331	304	7	1482	1482	NUM
ejpam-6331	304	8	,	,	PUNCT
ejpam-6331	304	9	pages	page	NOUN
ejpam-6331	304	10	464–470	464–470	NUM
ejpam-6331	304	11	.	.	PUNCT
ejpam-6331	305	1	american	american	PROPN
ejpam-6331	305	2	institute	institute	PROPN
ejpam-6331	305	3	of	of	ADP
ejpam-6331	305	4	physics	physics	PROPN
ejpam-6331	305	5	,	,	PUNCT
ejpam-6331	305	6	2012	2012	NUM
ejpam-6331	305	7	.	.	PUNCT